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You can't map the natural numbers to the set of real numbers, but you can map the natural numbers to the fractional part of a single real number.
by Tainnor 2y ago
You can't map the natural numbers to the set of real numbers, but you can map the natural numbers to the fractional part of a single real number.
- defrost 2y agoHow would this work when mapping them to the fractional part of the real number 2 ? Collapsing a countably infinite set to 0 doesn't seem useful or reversable.
- gizmo686 2y agoThe integer part is easy, since we already have the integers. Once you have D=[0,1), then you can define R=ZxD. That is to say, this definition of R seperates out the integral and fractional components of every real number.
- Tainnor 2y agofun n => 0 I'm not sure what you're trying to disagree with here.