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An interesting consequence of this in proofs. You’ll see various proofs involving real numbers that must account for the fact that 0.999…=1.0. There are, of co
by klodolph 7y ago
An interesting consequence of this in proofs.
You’ll see various proofs involving real numbers that must account for the fact that 0.999…=1.0. There are, of course, many different ways to construct real numbers, and often it’s very convenient to construct them as infinite sequences of digits after the decimal. For example, this construction makes the diagonalization argument easier. However, you must take care in your diagonalization argument not to construct a different decimal representation of a number already in your list!
- rini17 7y agoI never understood the fixation on diagonalization. Why can't ever exist another way for mapping any set to countables?
- voxl 7y agoDiagnolization is a pretty deep argument about fixpoints, Godels incompleteness argument is essentially a diagnolization. So why wouldn't there be fascination?
- deleted 7y ago[deleted]
- rcxdude 7y agoThe point is that diagonalization works whatever map you have come up with: no matter how you construct your list of the reals, you can come up with another real not on the list.