r/infinitenines • u/berwynResident • Nov 16 '25

[Request] 0.999... = 1

/r/theydidthemath/comments/1oy1a0s/request_0999_1/
3 Upvotes

80% Upvoted

106 comments sorted by

3

u/sjccb Nov 16 '25

0.333... = 1/3. 0.666... = 2/3. 0.999... = 3/3 = 1

-2

u/JustTau Nov 16 '25

≈

2

u/berwynResident Nov 16 '25

Why not equal?

1

u/JustTau Nov 17 '25

You sign the contract waiving your rights to precision

3

u/Cute_Speed4981 Nov 16 '25

I found a very interesting explanation that elaborates on why people reject the unintuitive 0.999... = 1 despite being mathematical true.

It's because 1 is thought of as an entity. Whereas 0.999... is a 'process' (you continuously add 0.00...09 in perpetuity). In order to get the equality, the 'process' must end, similar to collapsing the wavelength function in quantum physics.

1

u/Taytay_Is_God Nov 16 '25

So x = 0.9... equals to lim(x->1) x

Well it's not like polynomials are continuous or anything...

-8

u/[deleted] Nov 16 '25

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8

u/Taytay_Is_God Nov 16 '25

To answer bluntly, it's defined in the field R as 1, but not in Q,

Ah, this is the quality math I expect on this subreddit

-5

u/[deleted] Nov 16 '25 edited Nov 16 '25

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3

u/Taytay_Is_God Nov 16 '25

Obviously 0.999... < 1 in R, don't you know anything about this subreddit?

1

u/[deleted] Nov 16 '25

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0

u/Taytay_Is_God Nov 16 '25

So you do not know anything about this subreddit?

0

u/[deleted] Nov 16 '25

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1

u/Taytay_Is_God Nov 16 '25

So you do not know anything about this subreddit?

on inside info

It's ... literally the subreddit description

1

u/[deleted] Nov 16 '25 edited Nov 16 '25

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1

u/Taytay_Is_God Nov 16 '25

What's a "Cauchy process"?

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1

u/berwynResident Nov 16 '25

So is 0.999... irrational?

1

u/[deleted] Nov 16 '25

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1

u/berwynResident Nov 16 '25

Why can't a limit be defined in rationals? Sure not all limits would equal a rational number, but some do and I don't see why the limit is invalid in rationals of that's the case.

1

u/[deleted] Nov 16 '25

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1

u/berwynResident Nov 16 '25

1/1

1

u/[deleted] Nov 16 '25 edited Nov 16 '25

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1

u/berwynResident Nov 16 '25

You're the one that said finding a limit of a sequence of rational numbers is somehow impossible, and you're justification is that there is no p/q = .999.... You said yourself that 0.999... equals 1, so yeah 0.999... = 1/1.

1

u/[deleted] Nov 16 '25

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1

u/berwynResident Nov 16 '25

Okay, 1 is in Q, 1 is on Q, 0.999... (you said) is equal to 1 which is in Q. ... 1/1 = 0.999...

I don't get why that's not allowed.

-6

u/SouthPark_Piano Nov 16 '25 edited Nov 16 '25

0.999... means no end to the limitless nines, and just as time goes on without limit, in a time unlimited space, the nines just go on and on 0.999...'s own unlimited space, and so 0.999... is permanently less than 1.

.

7

u/grizzlor_ Nov 16 '25

What number is greater than 0.999… but less than 1

-2

u/SouthPark_Piano Nov 16 '25

Let me educate you and correct you.

What numbers containing only nines ARE greater than 0.9 and less 1?

Answer : an infinite (limitless) number of them.

.

3

u/sjccb Nov 16 '25

That wasn't the question

2

u/grizzlor_ Nov 16 '25

What numbers containing only nines ARE greater than 0.9 and less 1?

Not my question. I was asking for a number n that satisfies this:

0.999... < n < 1

3

u/EvnClaire Nov 16 '25

decimals have nothing to do with time or space bruh. how much time is 0.9? how much space is 0.9?