5 ms·
.999... and 1 exist on a continuous line. If they are different numbers, name a number between them.
by twiceaday 6y ago
.999... and 1 exist on a continuous line. If they are different numbers, name a number between them.
- chottocharaii 6y ago? Just because there is nothing between two numbers does not mean the two numbers are equivalent. What nonsense is this
- MockObject 6y agoEither two numbers are equal, or they're not equal. (Unless we're calling into question the law of excluded middle, but must we?)
- momentbruh 6y agoThat is true for the reals
- Dylan16807 6y agoWithout using 9999..., please name any two real numbers that don't have a number in between.
- ben509 6y ago{ 0.999... | 1 } using surreal number notation.
- chithanh 6y agoThe Wikipedia article says how, you need a definition of real numbers that includes nonzero infinitesimals (IOW does not satisfy the Archimedian property). So let there be an ω with 0.999... = 1 - 1/ω. Then a number between 0.999... and 1 would be 1 - 0.5/ω.
- effie 6y agoHow do you know that 1/ω is not 0?