3*(1/3=.333...) => 1=.999...

acubed123
Posers and Puzzles 14 Feb '06 00:59
1. 14 Feb '06 00:59
1/3=.333....

now multiply both sides by three

...and 1 = .999....

no need for real analysis, group theory, topology, or set theory for that
2. 14 Feb '06 01:24
Wow! A third thread related to this little math problem.
I didn't know my little argument would become such a big deal.
3. sonhouse
Fast and Curious
14 Feb '06 01:29
Originally posted by acubed123
1/3=.333....

now multiply both sides by three

...and 1 = .999....

no need for real analysis, group theory, topology, or set theory for that
Does 0.333.. = more or less than 0.333...?
4. 14 Feb '06 02:07
Personally I like asking the question,

What number is between the two numbers 1 and .999....?

This number by definition would be the difference (subtraction).
5. 14 Feb '06 02:16
Originally posted by Bishopcrw
Personally I like asking the question,

What number is between the two numbers 1 and .999....?

This number by definition would be the difference (subtraction).
Ah, from calculus, to high school algebra, to elementary basic math... now we're speaking my language, and I agree.
6. 14 Feb '06 02:19
ok ok ok we get it, .9999999... = 1, etc. the proof is simple, any 9th grade math student is familiar with it.

.99999....=X
therefore:
10 times (.9999.....) = 10X
which equals:
9.9999.......=10X
so:
9.9999....minus x = 10x - x

which equals 9= 9X
so 9/9 = 9x/9
so 1 = X

get it?
7. 14 Feb '06 02:29
Originally posted by Drumbo
ok ok ok we get it, .9999999... = 1, etc. the proof is simple, any 9th grade math student is familiar with it.

.99999....=X
therefore:
10 times (.9999.....) = 10X
which equals:
9.9999.......=10X
so:
9.9999....minus x = 10x - x

which equals 9= 9X
so 9/9 = 9x/9
so 1 = X

get it?
I like your name.
8. Trains44
Full speed locomotiv
14 Feb '06 02:45
Originally posted by SJ247
I like your name.
I like yours too.ðŸ˜‰
9. 14 Feb '06 03:14
Originally posted by TRAINS44
I like yours too.ðŸ˜‰
ðŸ˜‰
10. 14 Feb '06 06:01
Originally posted by Bishopcrw
Personally I like asking the question,

What number is between the two numbers 1 and .999....?

This number by definition would be the difference (subtraction).
there is none ..... try it ðŸ˜‰
11. 14 Feb '06 15:191 edit
And Acubed gets the answer correct.

I thought a little rephrase would help some people with this. ðŸ˜‰

Thanks to Drumbo for taking up the cause.

I was about to revisit the old postulates and proofs to prove it out.

I was quite surprised at the outburst in the community about this.
12. TheMaster37
Kupikupopo!
15 Feb '06 09:402 edits
Originally posted by Bishopcrw
Personally I like asking the question,

What number is between the two numbers 1 and .999....?

This number by definition would be the difference (subtraction).
The difference you speak of is smaller than all positive numbers.

It is not a negative number. Let's call the difference X.

So we have
1) 0=X or 0 is smaller than X
2) X is smaller than p, for all positive numbers p.

Theorem: X=0.
Proof:

Let's assume X is NOT equal to zero. From 1) we infer then that 0 is smaller than X

Make P = 0.5 * X.

0 is smaller than P clearly.

But now we have a contradiction with 2)!

Our assumption must then be false.

So X=0.

QED

In words this means that the difference between 1 and 0.999... is zero, in other words the two numbers are equal.