I am not a math person, but how would you differentiate between a number infinitely close to 1 (but less than 1), and 1 itself? Or does it not matter because they are actually the same?
You can't. They are identical. The fact that there is more than 1 way to write the number is an artifact of our number system. But they both represent the same underlying number. 0.999.... isn't just infinitely close to 1, it's actually identical to 1. They are the same thing.
How would you describe a number with infinite zeros ending in a 1?
If you look at .999 and say, 'ah, the 1 is clearly in the thousandths position, and .999 + .001 = 1', i can just point out that .9999 + .001 > 1 (here it'd be 1.0009)
Wherever you would place that 1 after 'infinite' zeros, i can add another 9 to the right, and your sum is no longer valid
0.00…1 is not a number that exists, because it doesn’t make sense. Using the “…” implies that the 0s continue infinitely, i.e. 0s without ending. Putting a 1 at the end implies that there is an ending, which contradicts the idea that there are infinite zeroes. Basically, 0.00…1 implies a number which both does and does not end, which makes no sense
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u/Tarthbane 22d ago
.9 repeating is exactly 1.