[split] 0.999... equals 1

[Tiberius]

If the runner never stops running... then he will always be running more than before.

How can you have something without limit... and not be expanding? You say it is endless... and yet you also think it is constant? That which does not end, does not stop going, isn't that the idea of infinite...? That it doesn't ever end?

Again, we aren't talking about infinite values, we are talking about infinite lengths. The fact that there are an infinite amount of 9s on the end of the number does not mean the number is changing value. The fact that it is infinitely long is a constant.

.9 is less than .99, continuing to expand this brings you bigger and bigger numbers... while their increase is getting smaller and smaller. .9^ is a continual state of 'almost there's... in that it cannot converge with one lest it stop expanding.

Indeed, and yet you cannot have the infinity + 1th number of the sequence 0.9r, since it doesn't exist. The number 0.9r is the "last" number in that sequence (for sake of argument, since there isn't technically an end to the sequence, since 0.9r is infinitely long).

You are adding a ridiculous definition to infinite. Infinity is the concept of never-ending. In example: an infinite supply of food... is not necessarily an ever-increasing mountain of food... it could easily be a single banana that continuously replenishes itself.

Now you are talking about values again. Stop it.

If it is a misconception... then represent .9^ a different way in the decimal system. In fact, do something easier: represent .5 in a different way in the decimal system.

0.9r is represented as a 1 in the decimal system.
0.5 is represented as 0.49r in the decimal system.
Any other examples you'd like?

An infinitely long number would be infinitely large. This is because it is continuously getting bigger. I am contending that it is not a constant, because infinites cannot have constant value.

Please explain to me how you can even argue this!

1) 0.9r is an infinitely long number.
2) By definition, an infinitely large number cannot have a number of a value greater than it.
3) You argue that any infinitely long number is infinitely large.
4) Therefore by 3 and 2, 0.9r is infinitely large, and cannot possibly have a number larger than it.
5) 2 is a larger number than 0.9r.
6) Therefore either 0.9r isn't an infinitely long number (which it is by definition), or your assertion that all infinitely long numbers are infinitely large is wrong.
7) Since 0.9r is infinitely long by definition, your assertion is wrong.

Q.E.D

Infinity is not a value... it is a concept. And it has the effect of making what it is applied to endless. When you place endlessness on a value: you make the value endless.

We aren't placing it on the value, we are placing it on the length. The difference is so astronomically important I can't believe you still don't get this simple fact.

It applies perfectly to my point. Infinity is a concept... infinitely long, infinitely large, infinitely grave, infinitely dead, infinitely advanced... all of those are valid uses of the concept. It is an adjective... it modifies the meaning of that which it is defining.

In example, blue rock, blue sky, blue human, blue book, blue computer. The word blue modifies rock, sky, human, book, and computer. Infinity is no different. It is a concept, and not a number.

Yes, but each way you use it means something different. A blue book isn't equal to an blue computer, neither is an infinitely long number equal to an infinitely large number just by definition. The only case this applies to is 9r which is both infinitely long and also infinitely large.
never end.