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
Numbers can always get smaller or larger.
But if you have 1.000(infinity 0s) you can’t have a 1 at the end. There’s no end to infinity. So there’s nowhere to put the 1. It’s kind of like saying “After forever, you can book this hotel room for 1 week.” It doesn’t make sense to have forever plus one week. When does that week happen if it’s already forever? The hotel room can never be booked.
If you want to specify a whole lot of 0s, that’s fine. Maybe 1.00(1 million 0s) and then a 1. That’s a number. And you could always make it smaller by saying 1.00(2 million 0s) and then a 1. But if you ever have infinite, there can never be anything that comes after it. Because infinity has no end.
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