So you are basically saying that if you eat 1 apple, you haven't eat 1 apple, but 0,99999 apple, leaving a tiny piece of it on the table. Seriously, WTF... Guys, one is one.. You got one birthday a year right? Not 0,9999.
In addition, you would also have to conclude that 1.000...1=.999... (1.000...1 has infinitely many 0's followed by a 1). I would treat them the same mathematically due to them approaching 1, but I do not agree that they are identical. Practically, yes. Actually, no. I think 1.000...1>.999... By how much? An unimaginably small number.
The problem is that you can't actually use infinities because it is a concept, not a number. You have to use tricks like limits, which are approximations.
1. I disagree that .333... = 1/3. It approaches 1/3, but does not equal it.
2. Dealing with infinities - again, this is a limit where an infinite series (.9+.09+.009...) approaches the sum (1).
3. For the 10c-c part: do you do 9.999...-.9999... or do you do 9.999...-.999...? For the first, you get 8.9991. For the second you get 9. If you say neither, then you are probably subtracting infinities, which is kinda hard...
Also for this part: 10c-c=c(10-1)=c=.999... so you get back to the start.
0.333... is not equal to 1/3. 0.333.. approaches 1/3 as the number of decimal places approaches infinity, but is never equal to 1/3. That's why, in reality, 0.333...≈1/3. These "proofs" are important in understanding why we may use the approximation 0.999 for 1 etc but they are not proofs for 0.999... being equal to 1. You are trying to provide a limit to an indefinite process (i.e. 0.9999.... repeating "infinite" times) is all.
Calling .9999999999999999999999999999999999999999999999 a 1 just because you don't know how to write it as a fraction is just arrogant lol I say that sarcastically but you know what I mean..At the end of the day it's only called a 1 because the 9's are infinite but they'll never reach the 1, it's not meant to reach the one..
they will never be equal, cus .999... will always lack . ...1. i know that u will think i'm a brat, but think of it for a second. they are just very close to one another, but will never be equal cus .(9) will always lack . ...1
@AxxeelR8 another way to show that 0.9999999...=1 is that there is no real numbers between 0.9999.....9 and 1 as they are INFINITELY close to each other. by there not being a real number between 0.9999....9 and 1 using the definition of real numbers we can see that 0.99999....9 equals 1.
@AxxeelR8 another way to show that 0.9999999...=1 is that there is no real numbers between 0.9999.....9 and 1 as they are INFINITELY close to each other. by there not being a real number between 0.9999....9 and 1 using the definition of real numbers we can see that 0.99999....9 equals 1.
also i would have done the sum of an infinite series by breaking down 0.999999999....99 into
0.99999...999= 0.9+0.09+0.009+...
then summarise it into terms of a geometric series.
It just seems like common sense that infinity never ends. So, how does an infinite strand of .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999's
suddenly turn into 1? If I were to keep holding that 9 on my keyboard for ever and ever, yes the number would be close to one, but those 9's would never convert to 1.
that's the thing about math; it's considerably more true than common sense
and that string of 9s wouldn't "suddenly turn in to" a 1. but, a decimal point followed by an infinite string of 9s can be represented by 1, since they are equal (as I showed)
the limit of 1/n as n approaches infinity may be zero. but the value of the function 1/n never reaches zero, nor does n ever reach infinity, because that would mean that infinity took on an actual value.
.9999999999..... If infinite series of nines is never rounded, it would never be1 it would be .00000000001..... smaller forever. Are you saying that for all practical purposes they are equal or that they are just as equal as 1 = 1? if 1/1 = .999...repeating, I would believe this theory, but we know that's not true.
but the reason for the existence of .999 repeating is due to the idea that one does not know to which Third part receives the extra .001, therefore, there must be a created formula to solve that issue of the unknown greater piece compared to the other two-thirds part of the whole of 1.
What about the parabola example where the parabola gets closer and closer to 0 (or 1 in this case) , but never actually touches the line. I know that there are no numbers between .999 repeating, but by the parabola example it is hard to say they are the same exact thing. I would have to assume that they must be different numbers for this to be true. Also a calculator tells us that while 1/9 = .1111 repeating, 9/9 = 1( not .9999 repeating). Can anyone explain this?
@getonmylevel1on1 I suppose, but I still say my explanation makes more sense than all these elaborate theories. Some people really can't see the forest for the trees. .999 repeating never says 1. Sure, for all practical purposes they have the same mathematical value, but to see they are the same number is false. I am not a math major, but I know that .999 repeating represents a number that continues on forever getting closer to 1 with each 9. Because it gets closer forever, it is never 1.
@jehan60188 let's just say that 1 is represented by a finish line in a race. By reaching or surpassing this finish line, you win the race. If you need to get to a number equal to or greater than one, of course 1.1 or 1.2 is sufficient as is 1. Now, along comes .999 repeating. It moves closer to the finish line for all eternity trying to reach 1, but...... it never does. Don't you see that even though the difference between them is unmeasurable, they are not the same thing.
@Baxteronsteroids that's one way to interpret the sequence proof. but consider the opposite- if I wanted to go from 1 to .999... how big of a step would i take? can that step be divided in half (i.e. can i take a smaller step)?
and what about the fractions, or algebra proof? those are not analogous to your "finish line" allegory.
So you are basically saying that if you eat 1 apple, you haven't eat 1 apple, but 0,99999 apple, leaving a tiny piece of it on the table. Seriously, WTF... Guys, one is one.. You got one birthday a year right? Not 0,9999.
GozillaFireschocks 3 weeks ago
Well, 1-0.999... = 0.000...1 0.000...1 being infinitely small is equal to 0 therefore 1=0.9999... but infinity isn't real, point at it! :)
Rubenite22mg 7 months ago
In addition, you would also have to conclude that 1.000...1=.999... (1.000...1 has infinitely many 0's followed by a 1). I would treat them the same mathematically due to them approaching 1, but I do not agree that they are identical. Practically, yes. Actually, no. I think 1.000...1>.999... By how much? An unimaginably small number.
The problem is that you can't actually use infinities because it is a concept, not a number. You have to use tricks like limits, which are approximations.
xanakoj 7 months ago
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1. I disagree that .333... = 1/3. It approaches 1/3, but does not equal it.
2. Dealing with infinities - again, this is a limit where an infinite series (.9+.09+.009...) approaches the sum (1).
3. For the 10c-c part: do you do 9.999...-.9999... or do you do 9.999...-.999...? For the first, you get 8.9991. For the second you get 9. If you say neither, then you are probably subtracting infinities, which is kinda hard...
Also for this part: 10c-c=c(10-1)=c=.999... so you get back to the start.
xanakoj 7 months ago
Comment removed
xanakoj 7 months ago
0.333... is not equal to 1/3. 0.333.. approaches 1/3 as the number of decimal places approaches infinity, but is never equal to 1/3. That's why, in reality, 0.333...≈1/3. These "proofs" are important in understanding why we may use the approximation 0.999 for 1 etc but they are not proofs for 0.999... being equal to 1. You are trying to provide a limit to an indefinite process (i.e. 0.9999.... repeating "infinite" times) is all.
elborrador 10 months ago
Comment removed
pose15 1 year ago
Calling .9999999999999999999999999999999999999999999999 a 1 just because you don't know how to write it as a fraction is just arrogant lol I say that sarcastically but you know what I mean..At the end of the day it's only called a 1 because the 9's are infinite but they'll never reach the 1, it's not meant to reach the one..
blackberrydro 1 year ago
@blackberrydro
infinite can't end in a 9 because it never ends, so it won't ever be just a number then.
daxster25 10 months ago
here's another neat "proof" that actually convinces a lot of people
suppose that .99...is not equal to one, well then take the average of the two, it's strictly greater than .99... and strictly less than 1, right?
how would you write that number?
Cabernal 1 year ago 4
they will never be equal, cus .999... will always lack . ...1. i know that u will think i'm a brat, but think of it for a second. they are just very close to one another, but will never be equal cus .(9) will always lack . ...1
AxxeelR8 1 year ago
@AxxeelR8 there is no such thing as ". ...1"
think about it if ". ...1" exists then ". ...1000001" exists and also ". ...1...154" exists
and unity minus any of those numbers will be less than .999...
jehan60188 1 year ago 2
@AxxeelR8 another way to show that 0.9999999...=1 is that there is no real numbers between 0.9999.....9 and 1 as they are INFINITELY close to each other. by there not being a real number between 0.9999....9 and 1 using the definition of real numbers we can see that 0.99999....9 equals 1.
brissydhiller 9 months ago
@AxxeelR8 another way to show that 0.9999999...=1 is that there is no real numbers between 0.9999.....9 and 1 as they are INFINITELY close to each other. by there not being a real number between 0.9999....9 and 1 using the definition of real numbers we can see that 0.99999....9 equals 1.
also i would have done the sum of an infinite series by breaking down 0.999999999....99 into
0.99999...999= 0.9+0.09+0.009+...
then summarise it into terms of a geometric series.
brissydhiller 9 months ago
Comment removed
MASTURCHEEF001 2 weeks ago
@AxxeelR8 ok ok. i give up/ if 9/10 = 1 then i give up on math
AxxeelR8 2 weeks ago
Comment removed
Baxteronsteroids 2 years ago
It just seems like common sense that infinity never ends. So, how does an infinite strand of .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999's
suddenly turn into 1? If I were to keep holding that 9 on my keyboard for ever and ever, yes the number would be close to one, but those 9's would never convert to 1.
Baxteronsteroids 2 years ago
that's the thing about math; it's considerably more true than common sense
and that string of 9s wouldn't "suddenly turn in to" a 1. but, a decimal point followed by an infinite string of 9s can be represented by 1, since they are equal (as I showed)
jehan60188 2 years ago
the limit of 1/n as n approaches infinity may be zero. but the value of the function 1/n never reaches zero, nor does n ever reach infinity, because that would mean that infinity took on an actual value.
chukivano 2 years ago
.9999999999..... If infinite series of nines is never rounded, it would never be1 it would be .00000000001..... smaller forever. Are you saying that for all practical purposes they are equal or that they are just as equal as 1 = 1? if 1/1 = .999...repeating, I would believe this theory, but we know that's not true.
Baxteronsteroids 3 years ago
if we use your definition of .9 repeating, that is, . 9 = 1-X where X is 1/10^N = .0000...0001
then, as N goes to infinity, we see that 1/10^N goes to zero
therefore .9999 repeating = 1, even by your definition
jehan60188 3 years ago
@Baxteronsteroids I think you are failing to comprehend infinities in math... dont worry its flummoxed much greater minds :-)
pubuman 1 year ago
@pubuman Well the above comment was intended for you and not getonmylevel1on1.
Baxteronsteroids 1 year ago
Also, doesn't .3333 repeating only approximately equal 1/3?
Baxteronsteroids 3 years ago
do the long division and you'll see it's exact
jehan60188 3 years ago
yeah , agreed, .999 repeating equals one.
but the reason for the existence of .999 repeating is due to the idea that one does not know to which Third part receives the extra .001, therefore, there must be a created formula to solve that issue of the unknown greater piece compared to the other two-thirds part of the whole of 1.
PurePower025 3 years ago
What about the parabola example where the parabola gets closer and closer to 0 (or 1 in this case) , but never actually touches the line. I know that there are no numbers between .999 repeating, but by the parabola example it is hard to say they are the same exact thing. I would have to assume that they must be different numbers for this to be true. Also a calculator tells us that while 1/9 = .1111 repeating, 9/9 = 1( not .9999 repeating). Can anyone explain this?
Baxteronsteroids 3 years ago
not sure what parabola example you're talking about. can you give more information on it?
jehan60188 2 years ago
thank you, my friends are non believers, but do understand fundamental algebra and can't refute the facts.
getonmylevel1on1 3 years ago 6
@getonmylevel1on1 I suppose, but I still say my explanation makes more sense than all these elaborate theories. Some people really can't see the forest for the trees. .999 repeating never says 1. Sure, for all practical purposes they have the same mathematical value, but to see they are the same number is false. I am not a math major, but I know that .999 repeating represents a number that continues on forever getting closer to 1 with each 9. Because it gets closer forever, it is never 1.
Baxteronsteroids 1 year ago
@Baxteronsteroids can you give any information on the difference between 1 and .999...?
since it is a real number, clearly greater than zero, what is its square root?
can it be represented as a fraction?
jehan60188 1 year ago
@jehan60188 let's just say that 1 is represented by a finish line in a race. By reaching or surpassing this finish line, you win the race. If you need to get to a number equal to or greater than one, of course 1.1 or 1.2 is sufficient as is 1. Now, along comes .999 repeating. It moves closer to the finish line for all eternity trying to reach 1, but...... it never does. Don't you see that even though the difference between them is unmeasurable, they are not the same thing.
Baxteronsteroids 1 year ago
@Baxteronsteroids that's one way to interpret the sequence proof. but consider the opposite- if I wanted to go from 1 to .999... how big of a step would i take? can that step be divided in half (i.e. can i take a smaller step)?
and what about the fractions, or algebra proof? those are not analogous to your "finish line" allegory.
jehan60188 1 year ago