0.999...ad infinitum does NOT Equal 1!

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Avatar of Elder_Knight

Using the " ... " notation to indicate repeating digits, if ...

0.111111... = 1/9
0.222222... = 2/9
0.333333... = 3/9 = 1/3
0.444444... = 4/9
0.555555... = 5/9
0.666666,,, = 6/9 = 2/3
0.777777... = 7/9
0.888888... = 8/9
... then ...
0.999999... = 9/9 = 1

Make sense?

Avatar of MarkoHoog

#45 flawed logic saying 9≠10 is correct but then extending this to 0.9recurring is incorrect since there are an infinite number of 9s in one. Add .9recurring to any of your examples for it to be correct.

Avatar of MarkoHoog

#47 wrong ⅔ is widely accepted as 0.6recurring you are just rounding it so that you cannot add ⅓ to find that 3/3=0.9recurring=1

Avatar of One_Zeroth

As n approaches Infinity

((10^n)-1))/(10^n) shall not reach 1.

As is true of 0.999 ad infinitum, which some here have argued against

Avatar of One_Zeroth

Once again,

I WON!

Avatar of SwordofSouls2023

0.9999 repeating infinitely and 1 are the same thing because there is just no room for some number in the middle

Avatar of One_Zeroth

((10^n)-1)/(10^n) never diverges to 1.

Case closed!

Avatar of SwordofSouls2023

no

Avatar of SwordofSouls2023

give me another proof

Avatar of One_Zeroth

That theory is validly presented.

Avatar of DeltaCrimson
One_Zeroth wrote:

As n approaches Infinity

((10^n)-1))/(10^n) shall not reach 1.

As is true of 0.999 ad infinitum, which some here have argued against

As 'n' approaches infinity , value of the above expression becomes infinity/infinity = 1

Avatar of batmann11111

-1?

Avatar of DeltaCrimson

Infinity - ( a finite constant )= infinity

Avatar of DeltaCrimson

Therefore infinity -1 = infinity

Avatar of MarkoHoog

How exactly does @One_Zeroth explain ⅓ being 0.333recurring if 0.999recurring is not 1?

Avatar of DiogenesDue

The OP already lost this argument a couple months ago...

https://www.chess.com/forum/view/off-topic/999-repeating-equals-1-89355481

Avatar of DiogenesDue

https://en.wikipedia.org/wiki/0.999.

Avatar of One_Zeroth
DeltaCrimson wrote:
One_Zeroth wrote:

As n approaches Infinity

((10^n)-1))/(10^n) shall not reach 1.

As is true of 0.999 ad infinitum, which some here have argued against

As 'n' approaches infinity , value of the above expression becomes infinity/infinity = 1

infinity/infinity does not only equal 1, it is also 2, and 3^(1/6) or any positive real.

Avatar of DiogenesDue

Still wrong as ever.

Avatar of One_Zeroth

YES!!

So what you are arguing about is that infinity/infinity is any positive.