[split] 0.999... equals 1

[Violet]

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.

Didn't I just explain this? Infinite = infinite. It is the same concept. If something is endlessly long, then it will continue to increase in size, as you cannot increase length without increasing size (Which is L*W*H).

The fact that there are infinite .1s, .9s, or .14637281946827s doesn't change the fact that the value is endlessly getting longer (and as a result: bigger).

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).

An infinite number is still a number. oo + 1 is an expression like any other... but it is unsolvable because of the nature of infinity. If you thin about it, A + 1 is just as impossible to solve. However, by giving value to A... we can solve it. Infinity cannot be given a simple value though... because it is endlessly changing value. For example, take oo + 1 - oo = 1, because we cancelled out that which previously could not be solved. The number of oo + 1 exists... but it cannot be calculated.

Now you are talking about values again. Stop it.

How do you mean?

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?

They are not equivalent. I think we are discussing this?

Please explain to me how you can even argue this!

1) 0.9r is an infinitely long number. yes.
2) By definition, an infinitely large number cannot have a number of a value greater than it. your misconception. If something is endlessly getting bigger... then it is endlessly big. .9 < .99 < .999 = infinite increase in size. It is endlessly growing bigger, and it is big without limit... therefore infinitely big. It is endlessly big, because it forever grows in size. That it never reaches an end means it is infinite.

Consider it also this way: When one says 'Infinity'... they usually are referring to a number of endless size. Endless ≠ greatest. That's how I can argue this.
3) You argue that any infinitely long number is infinitely large. It is.
4) Therefore by 3 and 2, 0.9r is infinitely large, and cannot possibly have a number larger than it. See bold after 2
5) 2 is a larger number than 0.9r. It is
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. See above.
7) Since 0.9r is infinitely long by definition, your assertion is wrong. See above

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.

There is no difference, once again. You can put it on a color, on how rocky something is, on a lot of things... and the concept of infinity does not change.

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.

The blueness of the computer is equal to the blueness of the book. The infiniteness of a length is equal to the infiniteness of a large number. Infinitely long denotes infinitely large, because size is Length*Width*Height, and something infinitely long Length^*Width*Height makes the size infinite.

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Wake up Saerules. He said the value isn't infinitely long, but the number is. If you don't know the difference between the two, you haven't been following the topic at all.A number IS a value by the definition of number

0.9r is a different numerical representation of the value 1. Not well enough justified for me to accept yet... although I have no doubt that the mathematicians are probably right

Now technically speaking, all numbers are infinitely long. The number line is infinite, and the value 2.5 is actually:

...0000000000000002.5000000000000... Zero is the value of nothingness. No value changes by adding zeros.

There are an endless number of 0s either side of the 2.5. Multiplying by 10 moves the decimal place to the right, dividing by 10 moves the decimal place to the left. Every number is infinitely long (in both directions) on the number line. The value isn't however.

00000.250000 is the same number as 0.25, because nothing changes when you add nothing... you are adding no description other than there isn't further description. You could call the number .25 'infinitely finite' if you don't want to just simplify it to being 'finite'. The number is the same number, and because of that: its value has not changed.

Edit reason: Trying out responding in a different way, needed to fix a number of things.