▲ 10 r/askmath
A question about real numbers and natural numbers.
It's already proven that there are more real numbers between 0 and 1 than there are natural numbers, but I'm confused about something
If a number can extend infinitely far in both directions from the decimal point, what's stopping us from, say, reversing the order of the digits so that every real number corresponds to the natural number that is that real number backwards? The tenths place of the real number becomes the ones place of the natural number, the hundredths place becomes the tens, and so on and so forth. Under this system, wouldn't we be able to map every real number 0<R<1 one-to-one with a natural number?
u/MinecraftIsMyLove — 1 day ago