One can divide by zero when one understands the difference between static quantity (incomplete) and dynamic quantity (1! complete). Integers referring to static quantity for equation solving purposes are illusory and incomplete - but when math as a system is considered, division by zero is a process like any other complete function. In the dynamic quantity, zero and infinity are, in fact, the same.
Well what this video states is that 1/lim x->0 is infinity, not that 1/0 is infinity, which isn't defined as infinity either but as undefined, singularity, etc.
Much simpler: if 1/0 should be infinity, why should -1/0 = 1/-0 = 1/0 be infinity but not -infinity which is NOT infinity? And one often forgets that there are no rules to calculate with infinity, not even that infinity * 0 = 0. It's getting worse when people think that e.g. for x -> infinity, 1/x * x converges to 0 because 1/x -> 0 and x -> infinity and 0 * infinity = 0... Common mistake!
In physics infinity is a recursive happening, it goes at a rate endlessly(or till the end of time), nothing at any point is known to be endless but rather know to be ever growing. So 1/0, so 0+0=0 so keep looping till you add enough 0's to get to 1, which in our system of physics and mathematics is endless, or at least until the end of time. Which for all we know could be endless.
I guess arithmetics is another story, though Scp1966 makes a good point, arithmetics only apply to finite numbers.
You can't say that 1/0 is not infinity because it doesn't make sense using a simple math rule. That math rule only aplies to finite numbers, like many others. For example: a+b=c does not apply to infinite amounts, because 1+infinity=infinity, which means a+b=b. Therefore, there is no reason to say that 1/0 is not infinity because of that consequence.
@Scp1966 Thanks for the comment. I don't really say that 1/0 is not infinity because of a simple math rule. I say that you can't divide by zero and that if you define 1/0 to be anything - even infinity - then we get problems.
I want to overcome students saying that 1/0 is obviously infinity. That we can't do ordinary arithmetic with infinity is a different problem. My treatment is incomplete but satisfies my requirement that students do not have to "unlearn" something later.
if we divide 1 by 0, the problem is: how many 0'.s are there in 1? adding trillions of trillions of trillions of trillions of trillions of 0's cannot be equal to 1. but adding an infinite number of 0's can equal 1, a result that is true but contradicts our common sense.
I found this to be absolutely wonderful and fun! Flawed, but still fun. It serves to remind people of how useful, and magical, math is.
Here's the flaw: the rule is 0 times x equals 0, and the contradiction of 0 x 1/0=1.
We are not multiplying simply 0 x 1/0. We are multiplying against infinity. therefor, it would need to be 0 x (1/0). then we'd still get the answer of 0.
This is similar to the fallacy reasoning of Fallacy of Composition. 1/0 requires notation when dealing with
@kurtwshrout Thanks for the comment. I don't think it's flawed. When we do algebra we want to know what a times b divided by a means. This gets tricky when a=0. By saying that we need special notation for dealing with 1/0 I feel that you are agreeing with me.
@DrKevinHouston Arithmetic allows us to cancel a * (b/a) because it equals to (a/a) * b. Since a/a = 1, when a is not 0, a/a * b = b. Therefore 0 * 1/0 will never be 1, since 0/0 = 0 and 0 * 1 = 0.
to continue my statement, since 0 is use to represent a very small no, and infinity is use to represent a very large no. therefore 0*infinity might give u B as well. Can you prove other wise?
0 is not a number. you cant cancel 0 with 0. 0 is use to represent a infinitely small number, but it is not a number. you can let A be infinitely small so A * (B/A) = B.
0 * infinity = 0 is an absolutely rubbish statement. How can you use it to justify anything. 0 is not a number and so is infinity. infinity is use to represent a VERY large number and 0 is use to represent a Very small number.
@liangying87 This is a big mistake. 0 doesn't represent an infinitely small number. It's the absence of anything. An infinitely small number is represented by negative infinity.
I think that people would've understood better if you took in account that 0 differs from 0m, the limit of an array that tends to 0. So 1 / 0m=inf but 1 / 0=undefined as it says in any book of math. Also "0 x inf=0" while "0m x inf=undetermined". Another reason why 1/0 is not inf is because basic operations between numbers can't result in symbols (inf). Since inf describes the result of limits for arrays, or recurrent relations.
@CaballusKnight Sorry I genuinely can't work out what "0m" and "1/0m=inf" mean. Since you claim the latter is any book of math can you give me a standard text and page number. Thanks!
@DrKevinHouston a) 1/0=undef I have said it's in any book, not 0m. b) 0m (notation may vary) is the limit of any array that tends to 0. We all say that lim(n->inf)1/x=0 but that's just a notation symbol, not the number 0, since that array it will never ever reach the number 0. In this case 0 and inf have the same nature of not being numbers. Just replace 0m with the limit of any array that tends to 0+ and you will understand what I was talking about.
@DrKevinHouston I gave you all the information needed to underline the difference between the number 0 and the limit 0. The rest lies in will, knowledge and power of understanding.
@CaballusKnight I had a genuine interest in trying to understand what you meant. If you do not wish to be understood, then that is your choice and I am 100% comfortable with that.
Your theory is nice but you have blown out years or research that have all been done by physicist and mathematicians. If a number divided by 0 isn't 0 then how do you explain gravitational singularities? yes your theory would make more sense if singularities didn't exist. those are the only known things to have infinite properties and all data backs up their existance and formation. meaning that a number divide by 0 truly does equal infinity.
@rocafella142 Thanks for the message. However, I stand by what I say. If you define 1/0 to be something, then you lose nice results like 0 times x equals x and b/a times a =b. I can explain gravitational singularities as a convenience used by physicists so that they can work with something they can't yet explain. I am not aware of any physical data that _proves_ the existence of an infinite quantity. If you have some then let me know. Thanks.
"those are the only known things to have infinite properties" There is nothing in this Universe that can have an infinite value and I can prove to you that if you consider something as infinite, that something has to be abstract (including time and space). Gravitational singularities are a result of gen. relativity and NOT a measured or observed phenomena since you can't observe nothing past the event horizon of black holes.
@rocafella142 The centre of a black hole is where the really tiny meets the really big, so Gen. Relativity intersects with Q Mechanics and things don't make sense. String Theory will try to answer this issue. Considering Gen Relativity the reason why a critical mass condense to an infinitesimal point it's because it doesn't encounter constraints, but as we go to the really tiny gravity and matter stop behaving continuously and enter on the realm of discrete values (QM).
@Scp1966 This still suffers from the problem mentioned in the video. What is the rule for 0 times x? The rule should be 0 times x equals 0. What is the rule for a times b/a? We should be able to cancel, so a times b/a = b. Thus 0 times b/0 should be b. This contradicts the zero times rule. Hence defining b/0 to be something (whether b is positive or negative) leads to the loss of a good rule!
Here are some words from a 16 years-old portuguese student:
What you say is not that 1/0 is not infinity. What you say is that when you multiply 0 by infinity, there is no result. What you say is: 0*infinity is not 0, but is not infinity either.
You do break some rules with this euation:
- Any number multiplied by 0 equals 0, but any number multiplied by infinity equals infinity. Therefore, these can not be factored one with each other.
@Scp1966 Obrigado pelo comentario. I really am saying that 1/0 is not infinity because I am saying that we can't define 1/0 to be something meaningful. If it can't be something, then certainly it can't be infinity. It is however what lots of students think 1/0 is.
One can divide by zero when one understands the difference between static quantity (incomplete) and dynamic quantity (1! complete). Integers referring to static quantity for equation solving purposes are illusory and incomplete - but when math as a system is considered, division by zero is a process like any other complete function. In the dynamic quantity, zero and infinity are, in fact, the same.
djlivingfire 4 months ago
Well what this video states is that 1/lim x->0 is infinity, not that 1/0 is infinity, which isn't defined as infinity either but as undefined, singularity, etc.
>: 8
his1nightmare 4 months ago
How would you illustrate a wave of the tan function as it gets near π/2, ie when sin is close to one and cos is close to zero?
GuythePikey 5 months ago
@GuythePikey By drawing the line of the graph tending to +/- infinity.
DrKevinHouston 5 months ago
Much simpler: if 1/0 should be infinity, why should -1/0 = 1/-0 = 1/0 be infinity but not -infinity which is NOT infinity? And one often forgets that there are no rules to calculate with infinity, not even that infinity * 0 = 0. It's getting worse when people think that e.g. for x -> infinity, 1/x * x converges to 0 because 1/x -> 0 and x -> infinity and 0 * infinity = 0... Common mistake!
leemes08 5 months ago
@leemes08 Good points! I like your -infinity= infinity argument.
DrKevinHouston 5 months ago
Comment removed
devilpizza123 5 months ago
In physics infinity is a recursive happening, it goes at a rate endlessly(or till the end of time), nothing at any point is known to be endless but rather know to be ever growing. So 1/0, so 0+0=0 so keep looping till you add enough 0's to get to 1, which in our system of physics and mathematics is endless, or at least until the end of time. Which for all we know could be endless.
I guess arithmetics is another story, though Scp1966 makes a good point, arithmetics only apply to finite numbers.
ov3rcl0cked 6 months ago
You can't say that 1/0 is not infinity because it doesn't make sense using a simple math rule. That math rule only aplies to finite numbers, like many others. For example: a+b=c does not apply to infinite amounts, because 1+infinity=infinity, which means a+b=b. Therefore, there is no reason to say that 1/0 is not infinity because of that consequence.
Scp1966 7 months ago
@Scp1966 Thanks for the comment. I don't really say that 1/0 is not infinity because of a simple math rule. I say that you can't divide by zero and that if you define 1/0 to be anything - even infinity - then we get problems.
I want to overcome students saying that 1/0 is obviously infinity. That we can't do ordinary arithmetic with infinity is a different problem. My treatment is incomplete but satisfies my requirement that students do not have to "unlearn" something later.
DrKevinHouston 7 months ago
@DrKevinHouston who did ever say, that 1/0 is infinity? Oo you CAN'T devide by zero because it's undefined, no matter which number you devide by zero
RockHailand 7 months ago
if we divide 1 by 0, the problem is: how many 0'.s are there in 1? adding trillions of trillions of trillions of trillions of trillions of 0's cannot be equal to 1. but adding an infinite number of 0's can equal 1, a result that is true but contradicts our common sense.
equationist 7 months ago
@DrKevineHouston
I found this to be absolutely wonderful and fun! Flawed, but still fun. It serves to remind people of how useful, and magical, math is.
Here's the flaw: the rule is 0 times x equals 0, and the contradiction of 0 x 1/0=1.
We are not multiplying simply 0 x 1/0. We are multiplying against infinity. therefor, it would need to be 0 x (1/0). then we'd still get the answer of 0.
This is similar to the fallacy reasoning of Fallacy of Composition. 1/0 requires notation when dealing with
kurtwshrout 7 months ago
@kurtwshrout Thanks for the comment. I don't think it's flawed. When we do algebra we want to know what a times b divided by a means. This gets tricky when a=0. By saying that we need special notation for dealing with 1/0 I feel that you are agreeing with me.
DrKevinHouston 7 months ago
@DrKevinHouston Arithmetic allows us to cancel a * (b/a) because it equals to (a/a) * b. Since a/a = 1, when a is not 0, a/a * b = b. Therefore 0 * 1/0 will never be 1, since 0/0 = 0 and 0 * 1 = 0.
JustWiseon3 6 months ago
@JustWiseon3 But surely x/x=1. So why do you say 0/0=0? After all, if 0*1=0 as you say as well, then dividing both sides by 0 should give 1.
DrKevinHouston 6 months ago
Don't show this to Chuck Norris!
heavymetaldeath4life 8 months ago
You are smart.
FenBolds 8 months ago
to continue my statement, since 0 is use to represent a very small no, and infinity is use to represent a very large no. therefore 0*infinity might give u B as well. Can you prove other wise?
liangying87 8 months ago
@liangying87 sorry but 0 is 0. a small number is something like x in lim x->0 1/x
delameu 8 months ago
0 is not a number. you cant cancel 0 with 0. 0 is use to represent a infinitely small number, but it is not a number. you can let A be infinitely small so A * (B/A) = B.
0 * infinity = 0 is an absolutely rubbish statement. How can you use it to justify anything. 0 is not a number and so is infinity. infinity is use to represent a VERY large number and 0 is use to represent a Very small number.
liangying87 8 months ago
@liangying87 0 is a number.
DrKevinHouston 8 months ago 2
@liangying87 This is a big mistake. 0 doesn't represent an infinitely small number. It's the absence of anything. An infinitely small number is represented by negative infinity.
Scp1966 7 months ago
The symbol ∞ is known as the lemniscate.
11889music 8 months ago
I think that people would've understood better if you took in account that 0 differs from 0m, the limit of an array that tends to 0. So 1 / 0m=inf but 1 / 0=undefined as it says in any book of math. Also "0 x inf=0" while "0m x inf=undetermined". Another reason why 1/0 is not inf is because basic operations between numbers can't result in symbols (inf). Since inf describes the result of limits for arrays, or recurrent relations.
CaballusKnight 8 months ago
@CaballusKnight Sorry I genuinely can't work out what "0m" and "1/0m=inf" mean. Since you claim the latter is any book of math can you give me a standard text and page number. Thanks!
DrKevinHouston 8 months ago
@DrKevinHouston a) 1/0=undef I have said it's in any book, not 0m. b) 0m (notation may vary) is the limit of any array that tends to 0. We all say that lim(n->inf)1/x=0 but that's just a notation symbol, not the number 0, since that array it will never ever reach the number 0. In this case 0 and inf have the same nature of not being numbers. Just replace 0m with the limit of any array that tends to 0+ and you will understand what I was talking about.
PS: Also ln(0)=-inf is wrong too.
CaballusKnight 8 months ago
@CaballusKnight Sorry, I still don't understand what the m signifies. Please define or give a page reference in a standard text.
DrKevinHouston 7 months ago
@DrKevinHouston I gave you all the information needed to underline the difference between the number 0 and the limit 0. The rest lies in will, knowledge and power of understanding.
CaballusKnight 7 months ago
@CaballusKnight I had a genuine interest in trying to understand what you meant. If you do not wish to be understood, then that is your choice and I am 100% comfortable with that.
DrKevinHouston 7 months ago
IM ONLY 12 M BRAID+_^&^# HURTSZEDD
thomasl4d 11 months ago
Your theory is nice but you have blown out years or research that have all been done by physicist and mathematicians. If a number divided by 0 isn't 0 then how do you explain gravitational singularities? yes your theory would make more sense if singularities didn't exist. those are the only known things to have infinite properties and all data backs up their existance and formation. meaning that a number divide by 0 truly does equal infinity.
rocafella142 1 year ago
@rocafella142 Thanks for the message. However, I stand by what I say. If you define 1/0 to be something, then you lose nice results like 0 times x equals x and b/a times a =b. I can explain gravitational singularities as a convenience used by physicists so that they can work with something they can't yet explain. I am not aware of any physical data that _proves_ the existence of an infinite quantity. If you have some then let me know. Thanks.
DrKevinHouston 1 year ago
@rocafella142
"those are the only known things to have infinite properties" There is nothing in this Universe that can have an infinite value and I can prove to you that if you consider something as infinite, that something has to be abstract (including time and space). Gravitational singularities are a result of gen. relativity and NOT a measured or observed phenomena since you can't observe nothing past the event horizon of black holes.
CaballusKnight 8 months ago
@CaballusKnight so what do you think is in the middle of a black hole then if it's not a singularity?
rocafella142 8 months ago
@rocafella142 The centre of a black hole is where the really tiny meets the really big, so Gen. Relativity intersects with Q Mechanics and things don't make sense. String Theory will try to answer this issue. Considering Gen Relativity the reason why a critical mass condense to an infinitesimal point it's because it doesn't encounter constraints, but as we go to the really tiny gravity and matter stop behaving continuously and enter on the realm of discrete values (QM).
CaballusKnight 8 months ago
@CaballusKnight so in other words you don't know?
rocafella142 8 months ago
I think that a number divided by 0 equals:
- Positive infinity, if x is positive;
- Negative infinity, if x is negative;
- Nothing, if the equation is 0/0. Too many rules would be accepted: x/x equals 1, 0/x equals 0, etc.
This is only my opinion. If you think I have a good idea about the division of 0, please let me know.
Scp1966 1 year ago
@Scp1966 This still suffers from the problem mentioned in the video. What is the rule for 0 times x? The rule should be 0 times x equals 0. What is the rule for a times b/a? We should be able to cancel, so a times b/a = b. Thus 0 times b/0 should be b. This contradicts the zero times rule. Hence defining b/0 to be something (whether b is positive or negative) leads to the loss of a good rule!
DrKevinHouston 1 year ago
Here are some words from a 16 years-old portuguese student:
What you say is not that 1/0 is not infinity. What you say is that when you multiply 0 by infinity, there is no result. What you say is: 0*infinity is not 0, but is not infinity either.
You do break some rules with this euation:
- Any number multiplied by 0 equals 0, but any number multiplied by infinity equals infinity. Therefore, these can not be factored one with each other.
Scp1966 1 year ago
@Scp1966 Obrigado pelo comentario. I really am saying that 1/0 is not infinity because I am saying that we can't define 1/0 to be something meaningful. If it can't be something, then certainly it can't be infinity. It is however what lots of students think 1/0 is.
DrKevinHouston 1 year ago
This is well-detailed and easy to understand! Thanks!
MagicEveryDay 1 year ago