There isn't any difference in the infinity concept, but you seem to repeatedly confuse the context in which the infinity is used; hence me repeatedly telling you so.
The difference in context is very important. An infinitely large number cannot have any number larger than it. An infinitely long number cannot have any number longer than it (and for sake of argument, we call all infinitely long numbers the same length so it doesn't contradict the definition).
Nobody is trying to turn an infinite into a finite, but you can use induction (and common sense) to show that since:
0.9 - 0.9 = 0
0.99 - 0.99 = 0
0.999 - 0.999 = 0
that if you continually add 9's to each side, you will get the same result...0.
0.999... - 0.999... is no different. Now I'll admit, I made a mistake earlier in the topic (way back) when I said that "infinity - infinity = 0". I wasn't thinking right at the time and was trying to get across another concept all together. However, this context is entirely different, and it matters not that infinity - inifinity =/= 0 for the proofs provided. This isn't about the subtraction of infinite numbers, but the subtraction of infinitely long numbers.
We can perfectly represent 1/3 and 1/7 in decimal. 1/3 = 0.333... and 1/7 = 0.142857... (repeating 142857). I fail to see why the fact that these numbers are infinitely long means they are inaccurate.
The difference in context is very important. An infinitely large number cannot have any number larger than it. An infinitely long number cannot have any number longer than it (and for sake of argument, we call all infinitely long numbers the same length so it doesn't contradict the definition).
Nobody is trying to turn an infinite into a finite, but you can use induction (and common sense) to show that since:
0.9 - 0.9 = 0
0.99 - 0.99 = 0
0.999 - 0.999 = 0
that if you continually add 9's to each side, you will get the same result...0.
0.999... - 0.999... is no different. Now I'll admit, I made a mistake earlier in the topic (way back) when I said that "infinity - infinity = 0". I wasn't thinking right at the time and was trying to get across another concept all together. However, this context is entirely different, and it matters not that infinity - inifinity =/= 0 for the proofs provided. This isn't about the subtraction of infinite numbers, but the subtraction of infinitely long numbers.
We can perfectly represent 1/3 and 1/7 in decimal. 1/3 = 0.333... and 1/7 = 0.142857... (repeating 142857). I fail to see why the fact that these numbers are infinitely long means they are inaccurate.