Interesting point and counterpoints which I am not sure I follow well. But ..
How do you "add" to anything without thinking what is being added to is in discreet unit/s ? (ie. numbered) . You can or cannot "add" to Inifinity ? That's the argument here ? My initial intuitive thought is to "add" is to encrease, period.
@Ear4Beauty Well, you could "add" the set of even numbers to the set of odd numbers in order to produce the set of Natural numbers, for example. The funny thing is that you could, in one sense, argue that you have increased something. After all, there are numbers in the set of Natural numbers that don't exist in the set of odd or that of even numbers. But yet, all these sets are infinitely countable, and in that sense they are "equivalent" to each other, in cardinality at least.
it should be emphasized that the definition of an infinite set is a set which is not finite. Therefore, the fundamental quality of infinite sets is that it is a set S for which there does not exist a bijection between S and a section of the positive integers {1, ... , N} for some N.
"All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe...."
Sounds like a convoluted way to rationalize dropping out of college. Pure drivel.
I disagree. In my computer science degree we studied computability in the 3rd year - in relation to different sizes of infinity and Turing machines. It was the hardest class I've ever done, and was very interesting.
"All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe...."
Sounds like a convoluted way to rationalize dropping out of college. Pure drivel.
Not necessarily. Think for example about an infinite line on an infinite plane. There are an infinite number of points on that line. But there is infinitely MORE outside the line.
I'm thinking of the universe, 360 degrees in all directions from whatever your vantage point is, not a specific line thought of as a line with infinite characteristics.
of course if you are a theist then you probably do not include your concept of god within this infinity or the argument that is commonly used would be self defeating.
Wrong interpretation of my Comment. Pino was mentioning specific sets... lines without end. I mentioned the universe. I think of the universe as everything into infinity. How you could read my Comment and Respond like I had said something totally different than what I had said. It doesn't make a difference anyway. Mathematics doesn't prove or disprove some ''god'' entity anyway.
All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe. Various numerical observations are true, but what's the connection between these observations and the grand scheme of things. I suppose the human mind needs to dissect whatever elements of reality it can and make conclusions that it can base its concepts of reality on. For the limitations of man, it's fine, but reality transcends human perception.
Great video! But I have one remark: we can treat (indeed) "infinity" as a number. But, if we choose this point of view we should forget about common sense. Set theory includes successfully terms as "ordinal numbers" and "cardinal numbers" and both are infinity, in the precise sense that they are not finite. And they may be operated (+,*,-,/,etc...)
But you're right about v***** ^ about the bijection related concept of cardinality.
Yes, you can talk about the so-called "transfinite" numbers. But they aren't "numbers" in the usual sense of the word. Maybe that is part of the cause of all the confusion :-)
Someone saying that you cannot add to infinitiy is clearly referencing a different conception of infinity than that to which you are referring. In effect, they are *defining* the concept. If we're going to speak in terms of sets, then "infinite", in those terms, would refer to the set to which nothing can be added. It isn't standard usage in mathematics, but apparently it is someone's usage.
Well, as you know, you can't add elements to a set if they are already in it. So in theory, a set can't be added to if it already contains anything you might think of adding.
I won't claim that this is standard, Pino, but when it comes to topics like this... reality, first agents, etc., there doesn't seem to me to be any requirement that people stick to standards. There are no binding rules.
Sets don't change, though. If you "add" to a set, it becomes a different set. So even a set defined recursively is not a set that is being added to. All it's implicit elements are in it already.
If you start using *that* as a definition then, by definition, you cannot add to *any* set, because you would *always* change it into "another set". That is what "adding to a set" actually means.
Nope. What you in fact prove is that introducing the concept of "a set to which nothing can be added" it leads to a logical contradiction. And that, in turn, then proves that there is no such thing as "a set to which nothing can be added".
I don't see any contradiction. A set to which nothing can be added would simply be defined as the set without superset. It can include itself without a problem.
Yes, of course. But if the definition leads to a logical contradiction, the definition is internally inconsistent and can't be upheld. Just like a set of axioms is only useful if it leads to an internally consistent system.
How, for example, could you have a set without superset? It's like declaring some number to be the largest prime. Yes, you can declare it to be that, but then it'll all go horribly wrong, and you have to conclude that the assumption must have been false.
If you google phrases like "universal set", or "cardinality of the universal set", you'll find that within set theory, there are such ideas. There are set theories which do not a allow a maximum cardinal, and set theories which do.
I'm not a mathematician, Pino. My formal study of computer science related subjects amounts to about 30 units at the undergraduate level. From what I can gather, there isn't any intrinsic contradiction to the idea of a set with no superset (but trivially itself).
The situation is unlike that of a maximum prime, in that one can prove, as you did in your "boring" video, that there can be no maximum prime. (the video was not boring)
From the Harper Collins dictionary of mathematics:
Russel's Paradox: "The paradox in NAIVE SET THEORY that the class of all classes that are not members of themselves is a member of itself only if it is not, and is not only if it is; this undermines the intuitive belief in an all-inclusive universal class. The paradox was discovered by Bertrand Russel in the axiomatization of set theory proposed by Gottlob Frege."
Depends on what you mean by "universe". If you mean it literally as "all there is" then, of course, there is only one. If you mean it more like the thing we live in, then I have no idea.
Oh yeah, Could you add 1 to 435348753759131349519734836713846139310967713876903769036793067136713067106471386709376130671307709238916012123581358919825092350320632562523652635327653275165134751051561356137134761375537543071771156734674744874384334924289342823472943934382949343377617513984765137517384571341348561389651384951873456715983834134757141714747173776597657896965985782362747613739136915971358971349561349569186132452346124514146251561124345124525632532454535267346534689934934887382378736?
I dont like it when people use infinity arguments, because I really think that infinity cannot exist outside of mathematics. So unless someone can give an example of infinity outside of mathematics I dont think any argument regarding infinity is valid. It's purely something mathematical, it does not apply to natural things.
exactly my sentiment. It's an abstract idea that can be proven to exist, but only by using other abstract ideas, hence it remains abstract. It's only link to reality is that us real people can think in abstract terms.
How can you be so sure? Cantor showed us that it is something that can be manipulated, and if that is the case I see no reason why it cannot be actualised in some way. Not in our immediate experience, of course, but perhaps at a very fundamental level. The idea certainly wouldn't bother me.
It's possible, a better argument for infinity is the infinitesimally small, if that exists then there must be an infinite number of infinitesimally small measurements that exist. The impact on infinity on the human psyche is a mixed one, though, it inspires and deludes people. Look at the anarchists on youtube, they sort of believe that the world is infinite.
That's something like zeno's paradox. No you cannot divide any space into infinitely small pieces. at least in our current understanding of quantum mechanics there is a limit to smallness (is that word btw?) and I would be very surprised if this would ever change.
Again I cannot think of any possible example of an infinity which could exist in the natural world
You would have to show some actual evidence without appealing to abstract ideas and mathematics. I would be really surprised if there is anything in the universe which is infinite, I can't think of any example outside of mathematics
But who says our universe is all there is to reality? Maybe there are infinitely many "universes" making up the totality of reality. Maybe it's Russian dolls, all the way up and never ending. Who knows? I'm not going to dismiss the possibility just because in our local neighbourhood we can't see any examples of it.
haha ironicly,to me that sounds a little like,I can see no evidence that god exists, but that doesnt mean that he doesnt
Yes ofcourse Im not certain infinity doesnt exist, but I can see no reason to assume that infinity exists. It is really extreeemly hypothetical. And why assume that infinity exists in the first place, I know you had to to counter moistheman's argument but you have also used it in your bouncing ball video. I simply wouldnt assume that infinity exists in the first place
I'm not making any assumptions, Knowntje. I'm not saying that infinity DOES exist, I'm saying you can't count it out. Maybe it does, maybe it doesn't. I don't care.
But because you can't prove it doesn't, you cannot legitimately make a claim that depends its non-existence. And one of the arguments moistheman uses to support his claim - and he DOES make a claim - is that infinity cannot be realised. I show that you can't make that assumption, so he can't base his argument on that.
yeah in the context of the debate your argument is valid, I was more talking about infinity in general and infinity arguments when you are on the affirmative, but you are not on the affirmative in this debate and I understand that
Maybe there are an infinite number of universes, and that is an inspiring thought. I'm thinking too much about morality right now, and I feel belief in infinity plays a detrimental role in society overall. There may be infinite universes, but from a pragmatic human sense: is it more than entertainment?
Now we're in kurisu's house! I love infinty arguments - they're all basically ignore the mathematical nature of infinty and instead treat it as a layman's concept
I once had a creationist tell me that a probability was 1 in infinity! (I think he meant incredibly improbable)
People's ignorance of mathematics is truly stunning. I've just been on a forum where people are actually DENYING PROBABILITY because they just rolled 3 sixes on 3 dice!
Yeah, I saw that on TV. It actually reminded me a lot of my video "The 1024th Malteser". But of course his presentation is millions of times better than mine. That's why I'm in a shitty job and he's on TV. Ah well. :P
Yeah, 1 divided by infinity is not defined for most purposes. But mathematically, the common sense is right, the assertion "1 divided by infinity is equal zero" does make sense. One way to see this is to take the limit 1 divided by N as N tends to a big number. See what happens.
The Riemann sphere is a geometric model created in the XIX century that describes arithmetic in the presence of infinity. It is not some mathematical nonsense it has lots of applications in physics.
Haha. You needed to explain the basics of the set theory. All he needed to do is read any book about it or a Georg Cantor biography.
By the way, a christian mathematics professor had a dogma about the numbers (I don't remember his name). He couldn't accept the Cantor's discoveries and tried to make Cantor's life an hell.
You said that you can show that all countable sets can be put in one-one correspondence with one another. This is misleading. By definition countable sets are those which form an equivalence class with natural numbers. There is thus no proof in the sense of "you can show". Rather it follows from our definitions.
Also, I'm sure an explanation as to why we care about one-one correspondence would have been helpful.
That's not quite right. For instance, the set of Natural numbers is infinite, and so is the set of Real numbers, but the set of Reals has a greater "size" (cardinality). If you "add" some segment of the Real continuum to the infinite set of Natural numbers, you get a bigger set.
Indeed. The term "bigger" is a bit misleading, but you're right. The natural numbers, the integers, the rational numbers, all those sets have the same cardinality, but for the Real numbers you need to move beyond that.
One "minor quibble". You said that infinities aren't numbers. They are. Specifically, they are "transfinite numbers". You even admitted this yourself when you started talking about sets with an "infinite number of elements".
Yeah, but transfinite numbers aren't numbers like 1, 2, 3 etc are. It's difficult to explain that in English without getting oneself into quite a linguistic knot LOL
Yup. Or you can just use a formula that represents the whole of the traverse. E.g. the capital Sigma notation for sums with the counter going from 0 to infinity.
Interesting point and counterpoints which I am not sure I follow well. But ..
How do you "add" to anything without thinking what is being added to is in discreet unit/s ? (ie. numbered) . You can or cannot "add" to Inifinity ? That's the argument here ? My initial intuitive thought is to "add" is to encrease, period.
Ear4Beauty 10 months ago
@Ear4Beauty Well, you could "add" the set of even numbers to the set of odd numbers in order to produce the set of Natural numbers, for example. The funny thing is that you could, in one sense, argue that you have increased something. After all, there are numbers in the set of Natural numbers that don't exist in the set of odd or that of even numbers. But yet, all these sets are infinitely countable, and in that sense they are "equivalent" to each other, in cardinality at least.
rozeboosje 10 months ago
@Ear4Beauty This video may help: watch?v=TaW_E61vKFw
rozeboosje 10 months ago
it should be emphasized that the definition of an infinite set is a set which is not finite. Therefore, the fundamental quality of infinite sets is that it is a set S for which there does not exist a bijection between S and a section of the positive integers {1, ... , N} for some N.
attilitus 1 year ago
@attilitus True, but for what I'm discussing here it isn't that important.
rozeboosje 1 year ago
Compliments to your clarity!
RobertHaraldsen 2 years ago
Thank you
rozeboosje 2 years ago
Who's Mo? Where?
RobertHaraldsen 2 years ago
A user named moistheman
Should be pronounced "mo is the man" but... Moist He-man!?!? LOL
I just realised that the guy has since removed all his video responses. Oh the humanity.
rozeboosje 2 years ago
@_@
I came across this trying to find a video to help me understand Cardinalities.
My mind just asploded I think.
Back to my math hw. >______>;;
Randomninja47 2 years ago
LOL
Sorry!
rozeboosje 2 years ago
Lol it's okay. :)
I'm sure I could understand it if I didn't watch this while frustrated at my HW. Lol.
Randomninja47 2 years ago
:-)
Don't give up.
rozeboosje 2 years ago
"All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe...."
Sounds like a convoluted way to rationalize dropping out of college. Pure drivel.
analhemorrhage 3 years ago
LOL. Be nice now. Diesel is one of the good guys!
rozeboosje 3 years ago
I disagree. In my computer science degree we studied computability in the 3rd year - in relation to different sizes of infinity and Turing machines. It was the hardest class I've ever done, and was very interesting.
nr900 3 years ago
"All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe...."
Sounds like a convoluted way to rationalize dropping out of college. Pure drivel.
analhemorrhage 3 years ago
Infinity is endless, therefore includes everything and anything you'd wish to add to it already.
DieselBodine 4 years ago
Not necessarily. Think for example about an infinite line on an infinite plane. There are an infinite number of points on that line. But there is infinitely MORE outside the line.
rozeboosje 4 years ago
I'm thinking of the universe, 360 degrees in all directions from whatever your vantage point is, not a specific line thought of as a line with infinite characteristics.
DieselBodine 4 years ago
well then you are thinking of a specific set.
and have just proved rose's point.
of course if you are a theist then you probably do not include your concept of god within this infinity or the argument that is commonly used would be self defeating.
memoryofakiss 4 years ago
Wrong interpretation of my Comment. Pino was mentioning specific sets... lines without end. I mentioned the universe. I think of the universe as everything into infinity. How you could read my Comment and Respond like I had said something totally different than what I had said. It doesn't make a difference anyway. Mathematics doesn't prove or disprove some ''god'' entity anyway.
DieselBodine 4 years ago
so you just stated an all inclusive set.
i fail to see how that would invalidate any other sets that are infinite in nature.
or are you saying the number system is not infinite? seems to go against everything i have learned about math.
you can re define the word if you would like but ill stick to the accepted meaning thank you.
memoryofakiss 4 years ago
if you still wish to dispute this issue you could prove roseboosje's explaination wrong by listing every even number that exists.
memoryofakiss 4 years ago
All the abstract reasoning, no matter how accurate in its presumption, doesn't necessarily explain the totality of reality in an infinite universe. Various numerical observations are true, but what's the connection between these observations and the grand scheme of things. I suppose the human mind needs to dissect whatever elements of reality it can and make conclusions that it can base its concepts of reality on. For the limitations of man, it's fine, but reality transcends human perception.
DieselBodine 4 years ago
Great video! But I have one remark: we can treat (indeed) "infinity" as a number. But, if we choose this point of view we should forget about common sense. Set theory includes successfully terms as "ordinal numbers" and "cardinal numbers" and both are infinity, in the precise sense that they are not finite. And they may be operated (+,*,-,/,etc...)
But you're right about v***** ^ about the bijection related concept of cardinality.
berveiga 4 years ago
Yes, you can talk about the so-called "transfinite" numbers. But they aren't "numbers" in the usual sense of the word. Maybe that is part of the cause of all the confusion :-)
rozeboosje 4 years ago
Someone saying that you cannot add to infinitiy is clearly referencing a different conception of infinity than that to which you are referring. In effect, they are *defining* the concept. If we're going to speak in terms of sets, then "infinite", in those terms, would refer to the set to which nothing can be added. It isn't standard usage in mathematics, but apparently it is someone's usage.
papackar 4 years ago
How can you have a set to which nothing can be added? There is nothing in Set Theory that precludes you from adding to a set.
People have got themselves into quite a knot thinking about such concepts as "the set of all sets", which must somehow be an element of itself O_o
rozeboosje 4 years ago
Well, as you know, you can't add elements to a set if they are already in it. So in theory, a set can't be added to if it already contains anything you might think of adding.
I won't claim that this is standard, Pino, but when it comes to topics like this... reality, first agents, etc., there doesn't seem to me to be any requirement that people stick to standards. There are no binding rules.
papackar 4 years ago
But the moment you create that set, you've added something *new*. Which you can then add to the set. It's recursion.
No. That isn't going to wash.
rozeboosje 4 years ago
Sets don't change, though. If you "add" to a set, it becomes a different set. So even a set defined recursively is not a set that is being added to. All it's implicit elements are in it already.
papackar 4 years ago
If you start using *that* as a definition then, by definition, you cannot add to *any* set, because you would *always* change it into "another set". That is what "adding to a set" actually means.
rozeboosje 4 years ago
But the point is, recursive definition is not an issue. Any set you can think of would be a subset of THE set to which "nothing can be added".
"Adding to a set" just means describing a superset.
papackar 4 years ago
Nope. What you in fact prove is that introducing the concept of "a set to which nothing can be added" it leads to a logical contradiction. And that, in turn, then proves that there is no such thing as "a set to which nothing can be added".
rozeboosje 4 years ago
I don't see any contradiction. A set to which nothing can be added would simply be defined as the set without superset. It can include itself without a problem.
papackar 4 years ago
Yes, of course. But if the definition leads to a logical contradiction, the definition is internally inconsistent and can't be upheld. Just like a set of axioms is only useful if it leads to an internally consistent system.
How, for example, could you have a set without superset? It's like declaring some number to be the largest prime. Yes, you can declare it to be that, but then it'll all go horribly wrong, and you have to conclude that the assumption must have been false.
rozeboosje 4 years ago
If you google phrases like "universal set", or "cardinality of the universal set", you'll find that within set theory, there are such ideas. There are set theories which do not a allow a maximum cardinal, and set theories which do.
I'm not a mathematician, Pino. My formal study of computer science related subjects amounts to about 30 units at the undergraduate level. From what I can gather, there isn't any intrinsic contradiction to the idea of a set with no superset (but trivially itself).
papackar 4 years ago
The situation is unlike that of a maximum prime, in that one can prove, as you did in your "boring" video, that there can be no maximum prime. (the video was not boring)
papackar 4 years ago
There are variations of set theory - New Foundations, in which this is conceivable, but this does not appear to be internally consistent.
rozeboosje 4 years ago
How and why?
papackar 4 years ago
That's a good question, and that is where my knowledge ends :-)
rozeboosje 4 years ago
From the Harper Collins dictionary of mathematics:
Russel's Paradox: "The paradox in NAIVE SET THEORY that the class of all classes that are not members of themselves is a member of itself only if it is not, and is not only if it is; this undermines the intuitive belief in an all-inclusive universal class. The paradox was discovered by Bertrand Russel in the axiomatization of set theory proposed by Gottlob Frege."
papackar 4 years ago
Yes indeed
rozeboosje 4 years ago
I agree with you. You can coherently define the CLASS of all sets, but the SET of all sets is not a consistent idea.
This kind of reasoning is due to Hilbert (in order to solve the paradox created by himself)
This is the intuitive idea underlying the theory of types
berveiga 4 years ago
Thanks for the clarification!
rozeboosje 4 years ago
How many universes are there?
sarcasmosis 4 years ago
Depends on what you mean by "universe". If you mean it literally as "all there is" then, of course, there is only one. If you mean it more like the thing we live in, then I have no idea.
rozeboosje 4 years ago
435348753759131349519734836713846139310967713876903769036793 067136713067106471386709376130671307709238916012123581358919 825092350320632562523652635327653275165134751051561356137134 761375537543071771156734674744874384334924289342823472943934 382949343377617513984765137517384571341348561389651384951873 456715983834134757141714747173776597657896965985782362747613 739136915971358971349561349569186132452346124514146251561124 345124525632532454535267346534689934934887382378737
rozeboosje 4 years ago
Oh yeah, Could you add 1 to 435348753759131349519734836713846139310967713876903769036793067136713067106471386709376130671307709238916012123581358919825092350320632562523652635327653275165134751051561356137134761375537543071771156734674744874384334924289342823472943934382949343377617513984765137517384571341348561389651384951873456715983834134757141714747173776597657896965985782362747613739136915971358971349561349569186132452346124514146251561124345124525632532454535267346534689934934887382378736?
PinoX7 4 years ago
You typed #3 17.2% of the time and #7 13.2% and you rarely typed #0. Did you mainly use two fingers and are you left handed?
InfinitelyManic 4 years ago
wow your good, although not left handed, i did use my left hand.
PinoX7 4 years ago
I might need to make another infinity video sometime.
CousinoMacul 4 years ago
Yeah. That would be good!
rozeboosje 4 years ago
Agreed. Infinity is not a number, but a concept. Im always surprised at how many people do not get this.
TawntheAtheist 4 years ago
Yup
rozeboosje 4 years ago
Great first part, on to the second one...
TheKidFrom13thStreet 4 years ago
Cheers
rozeboosje 4 years ago
I dont like it when people use infinity arguments, because I really think that infinity cannot exist outside of mathematics. So unless someone can give an example of infinity outside of mathematics I dont think any argument regarding infinity is valid. It's purely something mathematical, it does not apply to natural things.
Knowntje 4 years ago
exactly my sentiment. It's an abstract idea that can be proven to exist, but only by using other abstract ideas, hence it remains abstract. It's only link to reality is that us real people can think in abstract terms.
gratex 4 years ago
So us, real people, can manipulate it in reality ... ;-)
rozeboosje 4 years ago
How can you be so sure? Cantor showed us that it is something that can be manipulated, and if that is the case I see no reason why it cannot be actualised in some way. Not in our immediate experience, of course, but perhaps at a very fundamental level. The idea certainly wouldn't bother me.
rozeboosje 4 years ago
It's possible, a better argument for infinity is the infinitesimally small, if that exists then there must be an infinite number of infinitesimally small measurements that exist. The impact on infinity on the human psyche is a mixed one, though, it inspires and deludes people. Look at the anarchists on youtube, they sort of believe that the world is infinite.
gratex 4 years ago
That's something like zeno's paradox. No you cannot divide any space into infinitely small pieces. at least in our current understanding of quantum mechanics there is a limit to smallness (is that word btw?) and I would be very surprised if this would ever change.
Again I cannot think of any possible example of an infinity which could exist in the natural world
Knowntje 4 years ago
You would have to show some actual evidence without appealing to abstract ideas and mathematics. I would be really surprised if there is anything in the universe which is infinite, I can't think of any example outside of mathematics
Knowntje 4 years ago
But who says our universe is all there is to reality? Maybe there are infinitely many "universes" making up the totality of reality. Maybe it's Russian dolls, all the way up and never ending. Who knows? I'm not going to dismiss the possibility just because in our local neighbourhood we can't see any examples of it.
rozeboosje 4 years ago
haha ironicly,to me that sounds a little like,I can see no evidence that god exists, but that doesnt mean that he doesnt
Yes ofcourse Im not certain infinity doesnt exist, but I can see no reason to assume that infinity exists. It is really extreeemly hypothetical. And why assume that infinity exists in the first place, I know you had to to counter moistheman's argument but you have also used it in your bouncing ball video. I simply wouldnt assume that infinity exists in the first place
Knowntje 4 years ago
I'm not making any assumptions, Knowntje. I'm not saying that infinity DOES exist, I'm saying you can't count it out. Maybe it does, maybe it doesn't. I don't care.
But because you can't prove it doesn't, you cannot legitimately make a claim that depends its non-existence. And one of the arguments moistheman uses to support his claim - and he DOES make a claim - is that infinity cannot be realised. I show that you can't make that assumption, so he can't base his argument on that.
rozeboosje 4 years ago
yeah in the context of the debate your argument is valid, I was more talking about infinity in general and infinity arguments when you are on the affirmative, but you are not on the affirmative in this debate and I understand that
Knowntje 4 years ago
Maybe there are an infinite number of universes, and that is an inspiring thought. I'm thinking too much about morality right now, and I feel belief in infinity plays a detrimental role in society overall. There may be infinite universes, but from a pragmatic human sense: is it more than entertainment?
gratex 4 years ago
Remember that this is a debate. See also my comment to Knowntje.
rozeboosje 4 years ago
Now we're in kurisu's house! I love infinty arguments - they're all basically ignore the mathematical nature of infinty and instead treat it as a layman's concept
I once had a creationist tell me that a probability was 1 in infinity! (I think he meant incredibly improbable)
kurisu313 4 years ago
LOL
rozeboosje 4 years ago
Then you get people who start saying one divided by infinity equals zero...
TawntheAtheist 4 years ago
People's ignorance of mathematics is truly stunning. I've just been on a forum where people are actually DENYING PROBABILITY because they just rolled 3 sixes on 3 dice!
kurisu313 4 years ago
Wow thats truly stupid.
Watch this guys stuff:
watch?v=lX94fV4TWbc
Derren Brown: The system.
The most unbelievably obvious piece of trickery using probability.. yet people fall for it. (Although I cant see how he does the photos thing..)
TawntheAtheist 4 years ago
Yeah, I saw that on TV. It actually reminded me a lot of my video "The 1024th Malteser". But of course his presentation is millions of times better than mine. That's why I'm in a shitty job and he's on TV. Ah well. :P
rozeboosje 4 years ago
Well, probability definitely doesn't exist in hindsight XD
rozeboosje 4 years ago
Yeah, 1 divided by infinity is not defined for most purposes. But mathematically, the common sense is right, the assertion "1 divided by infinity is equal zero" does make sense. One way to see this is to take the limit 1 divided by N as N tends to a big number. See what happens.
The Riemann sphere is a geometric model created in the XIX century that describes arithmetic in the presence of infinity. It is not some mathematical nonsense it has lots of applications in physics.
berveiga 4 years ago
Thanks!
rozeboosje 4 years ago
you're welcome!
berveiga 4 years ago
Haha. You needed to explain the basics of the set theory. All he needed to do is read any book about it or a Georg Cantor biography.
By the way, a christian mathematics professor had a dogma about the numbers (I don't remember his name). He couldn't accept the Cantor's discoveries and tried to make Cantor's life an hell.
pedroac 4 years ago
You can imagine why. It really screws up ontological arguments.
rozeboosje 4 years ago
You said that you can show that all countable sets can be put in one-one correspondence with one another. This is misleading. By definition countable sets are those which form an equivalence class with natural numbers. There is thus no proof in the sense of "you can show". Rather it follows from our definitions.
Also, I'm sure an explanation as to why we care about one-one correspondence would have been helpful.
neotropic9 4 years ago
Yeah, but I have to keep it short. By all means feel free to expand on this through a video response. Every little bit helps :-)
rozeboosje 4 years ago
You can add to infinities, but the size of the set doesn't change.
neotropic9 4 years ago
Exactly
rozeboosje 4 years ago
That's not quite right. For instance, the set of Natural numbers is infinite, and so is the set of Real numbers, but the set of Reals has a greater "size" (cardinality). If you "add" some segment of the Real continuum to the infinite set of Natural numbers, you get a bigger set.
papackar 4 years ago
Indeed. The term "bigger" is a bit misleading, but you're right. The natural numbers, the integers, the rational numbers, all those sets have the same cardinality, but for the Real numbers you need to move beyond that.
rozeboosje 4 years ago
One "minor quibble". You said that infinities aren't numbers. They are. Specifically, they are "transfinite numbers". You even admitted this yourself when you started talking about sets with an "infinite number of elements".
neotropic9 4 years ago
Yeah, but transfinite numbers aren't numbers like 1, 2, 3 etc are. It's difficult to explain that in English without getting oneself into quite a linguistic knot LOL
rozeboosje 4 years ago
Infinities can be traversed it just requires infinite steps.
neotropic9 4 years ago
Yup. Or you can just use a formula that represents the whole of the traverse. E.g. the capital Sigma notation for sums with the counter going from 0 to infinity.
rozeboosje 4 years ago
Very clear, my stomach is ready for more! ;)
0092b 4 years ago
yum! On its way, Sir!
rozeboosje 4 years ago