Re: The rational number 5 and the real number 5

On Mar 6, 2:48 am, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:

Of course 5 the integer, 5/1 the rational and 5.0000....
the real are not equal until you embed the integers
into the rationals and the rationals into the reals.

I don't see how, observing that there are different
constructions for numbers, we should then conclude
that those different constructions mean the numbers
resulting are somehow qualitatively different.

How is having two different constructions for five any
different from having two different expressions that
evaluate to five? Isn't 5/1 = 10/2? Isn't it just as much
the case that succ(succ(succ(succ(succ(0))))) = 10/2?
Even though the construction used on the left can only
construct naturals and the construction on the right
can construct any rational.

Is it possible this is exclusively a philosophical question?


Marshall
.

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