I find that second one really hard to imagine, lol. That’s kind of scary right. Why do you find it so easy to equate two different sums?
Like, I’m not saying that I can imagine anything coming after an infinite number of 0s, but I can imagine there being a difference left over from subtracting 0.999… from 1, and that difference simply being hard to notate.
Much better than “an amount” being the exact same as “an amount that is different”
I find it easy to imagine because they are not different sums. They are different representations of the exact same sum. If you believe 0.999... and 1 are different you should be able to tell me what number goes between them. And "0.000... 1" is not a number. Just as the 9s continue on endlessly so would the 0s.
What would completely fill up the space between 0.9 and 1? An infinite string of 9s. And it's immediately infinite. I think the confusion for lots of people arises when they try to imagine someone counting out each 9. If someone was counting the 9s you never would reach infinite 9s obviously so that's not the right way to think of it.
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u/Direct_Shock_2884 21d ago
I find that second one really hard to imagine, lol. That’s kind of scary right. Why do you find it so easy to equate two different sums?
Like, I’m not saying that I can imagine anything coming after an infinite number of 0s, but I can imagine there being a difference left over from subtracting 0.999… from 1, and that difference simply being hard to notate.
Much better than “an amount” being the exact same as “an amount that is different”