Turns out, dragons are kind of cool.

I am going to note that this was not well-expressed when you said ‘we can just pretend to have “reached infinity” and work with like any number’. To a lay person it would look as if you were suggesting that we non-rigorously treat one object (like the sequence (0.9, 0.99, 0.999,…)) as another (like the real number that that sequence converges to given the standard topology of the space of real numbers).

Yeah that’s something that people have to get used to in maths, if the limit of a sequence exists we can just pretend to have “reached infinity” and work with like any number

I’m not sure what you are trying to say here, and I have a background in math. I think this is just going to confuse lay people.

I will be posting another another proof, one using the assumption that 0.999… is the sum of the series 9/10+9/100+9/1000+… (and that 1 is the sum of the series 1+0+0+0+…), unless somebody else comes here and feeds it to the little guy first.

Four more years!

And like he also said, ‘Pause’.

A real number can’t be approaching anything. It is not a function or any other sort of object that can be said to be approaching anything.

So, under the relevant construction of the space of real numbers, every real number is an equivalence class of Cauchy sequences of rational numbers with respect to the relation R outlined in my comment. In other words, under this definition, a real number is an equivalence class that includes all such sequences that for every pair of them the relation R holds (and R is, indeed, an equivalence relation - it is reflexive, symmetric, and transitive, - that is not hard to prove).

We prove that, for the sequences (1, 1, 1,…) and (0.9, 0.99, 0.999,…), the relation R holds, which means that they are both in the same equivalence class of those sequences.

The decimals ‘1’ and ‘0.999…’, under the relevant definition, refer to numbers that are equivalence classes that include the aforementioned sequences as their elements. However, as we have proven, the sequences both belong to the same equivalence class, meaning that the decimals ‘1’ and ‘0.999…’ refer to the same equivalence class of Cauchy sequences of rational numbers with respect to R, i.e. they refer to the same real number, i.e. 0.999… = 1.

I suppose I will post one myself, as I do not expect anybody else to have that one in mind.

The decimals ‘0.999…’ and ‘1’ refer to the real numbers that are equivalence classes of Cauchy sequences of rational numbers (0.9, 0.99, 0.999,…) and (1, 1, 1,…) with respect to the relation R: (aRb) <=> (lim(a_n-b_n) as n->inf, where a_n and b_n are the nth elements of sequences a and b, respectively).

For a = (1, 1, 1,…) and b = (0.9, 0.99, 0.999,…) we have lim(a_n-b_n) as n->inf = lim(1-sum(9/10^k) for k from 1 to n) as n->inf = lim(1/10^n) as n->inf = 0. That means that (1, 1, 1,…)R(0.9, 0.99, 0.999,…), i.e. that these sequences belong to the same equivalence class of Cauchy sequences of rational numbers with respect to R. In other words, the decimals ‘0.999…’ and ‘1’ refer to the same real number. QED.

I agree, but the little guy does need rigour, or he will starve under crapitalism.

He’s hungry

Feed him

Am, unfortunately, not vegan in the sense of consuming meat and other animal-sourced food, despite agreeing with vegan positions.

Reason: am weak-willed. My attempts to stop have failed because of that ,essentially.

I console myself with the fact that the most important thing in this regard is for the relevant industries to be stopped, and that my individual activities wouldn’t be enough to stop the suffering of other animals for what is essentially our fun, but I do recognise myself as bad in this regard.

What do you mean the emperor is ‘naked’?

Are women bourgeois?

Not for the first time.

I post, therefore I am.

That’s because all they had for decades was the anti-consumer practice of console exclusivity. That has been the sole reason for the lack of some games on some of the platforms.

If Trump get back into office, I think I may permanently leave this country

Why haven’t you?

There is only Seksbjørnen.