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

acubed123

Posers and Puzzles

14 Feb 06

acubed123

Joined: 20 Dec 05
Moves: 1008

14 Feb 06

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

Bishopcrw

Joined: 07 Dec 05
Moves: 3685

14 Feb 06

Wow! A third thread related to this little math problem.
I didn't know my little argument would become such a big deal.

sonhouse

Fast and Curious

slatington, pa, usa

Joined: 28 Dec 04
Moves: 53336

14 Feb 06

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...?

Bishopcrw

Joined: 07 Dec 05
Moves: 3685

14 Feb 06

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).

SJ247

Joined: 05 Oct 05
Moves: 63425

14 Feb 06

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.

Drumbo

Joined: 05 Feb 06
Moves: 2712

14 Feb 06

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?

SJ247

Joined: 05 Oct 05
Moves: 63425

14 Feb 06

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.

Trains44

Full speed locomotiv

On tracks.

Joined: 03 Oct 04
Moves: 12831

14 Feb 06

Originally posted by SJ247
I like your name.

I like yours too.😉

SJ247

Joined: 05 Oct 05
Moves: 63425

14 Feb 06

Originally posted by TRAINS44
I like yours too.😉

😉

acubed123

Joined: 20 Dec 05
Moves: 1008

14 Feb 06

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 😉

Bishopcrw

Joined: 07 Dec 05
Moves: 3685

14 Feb 06

1 edit

And Acubed gets the answer correct.

I thought a little rephrase would help some people with this. 😉

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.

TheMaster37

Kupikupopo!

Out of my mind

Joined: 25 Oct 02
Moves: 20443

15 Feb 06

2 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.