Proof that 1 is Equal to .999999999........!

[tarheel91]

wfz said:

Shameless said:

wfz said:

Eab, the problem with the "infinity times zero" question is that infinity isn't even a number. Also most of the time you're looking at that, 0 isn't a number either. They're both behaviors.

@Shameless, 1/3 means "one third of". If you take .999999 = 1, then that's fine, since 1/3 of .999999 is .3333333

However if you don't, then 1/3 isn't exactly equal to .3333. It's more like .33333 1/3

=P

 

EDIT: Shameless, infinity times zero is not zero. Don't criticize people for butchering math and then do it yourself in the same post!

1/3 means 1 divided by 3 like all fractions.

Zero is always zero, no matter what you choose to multiply it by.

 

Zero is always zero, no matter what real number you multiply it by. Infinity is not a number, so that doesn't work.

 

Infinity is a behavior. Also, 0 can be a behavior as well, so using L'hopital's rule is great when you have infinities and zeroes.

 

I was under the impression that L'hopital's rule only worked when it was 0/0 or Infinity/Infinity.  It might change in later maths though; I don't know.  In Calculuas AB, that's how it is, at least.

 

Also, math isn't messed up.  .999... is the SAME number as 1.  A lot of people have trouble with this conceptually because we can't fathom infinity.  You can't look at this as approaching an infinite number of 9's (which would be less than 1) or anything like that.  The number of 9's in .999... has actually reached infinity.

Here's another way to prove it.

c = .999...

10c = 9.999...

10c - c = 9.999... - .999...

9c = 9

c = 1