u/MZDgamer88

100/10 + 1000/100 + 10000/1000 + etc = A

91/10 + 991/100 + 9991/1000 + etc = B

1. What is A?

2. What is B?

3. What is A - B?

Is there a better way to assign 0.999… a singular, meaningful, unique value other than by limits?

Even if you can’t accept that 0.999… = 1, surely you don’t expect us to accept that 0.999… is multiple values. That’s just ludicrous. Can you at least understand why we reject that?

In decimal notation, a single expression should represent a single constant value. Given that, what is it and why?

Is it desirable for them to be the same?

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Observe the following approximation of C:

2 - 0.999… = A

A^3 = B

B * 0.999… = C

C ≈ 1

What is the absolute error of my approximation of C?

If a tree falls in a forest that is infinitely far away, and no one is there to hear it, does it make a sound?

0.999…91 + 0.999…91 = 1.999…82

0.999…01 + 0.999…02 = 1.999…803 (different reference point

0.999…duck + 0.999…dog = 1.999…doguck

1.000…dog + 0.999…duck = 1.999…Duckog (with a capital 'D')

I guess my point is that there seems to be no application whatsoever for the idea that 1 ≠ 0.r9.

Can you think of any real applications?

Is it not enough that 1 is arithmetically indistinguishable from 0.r9 such that our definition for equality is consistent with 1 = 0.r9?