Can numbers get so small (or so large) that there is kind of a “planck length” effect where you just can’t get any smaller? Or is it really possible to have 1.000000…(infinite)1
EDIT: I know planck length is not a mathmatical function, I just used it as an anology for “smallest thing technically mesurable,” hence the quotation marks and “kind of.”
In: 87
You’re asking three different questions.
1. Yes, real numbers can be arbitrarily small or large, and integers can be arbitrarily large. Given any real number, you can divide it in half to get a smaller number, or double it to get a larger number. So there’s no limit on how small or large numbers can be.
2. The Planck length is a matter of physics, not mathematics. We *use* numbers in physics to describe things because they’re useful for that. But even if there is a limit to the indivisibility of the physical world, the real numbers have no such limit.
3. There is no real number “1.000000…(infinite)1”. That’s not meaningful notation. You can make a real number *arbitrarily* small, but not *infinitely* small. This may seem like a technical nitpick, but it’s very important.
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