A Mathematical Prelude to the Philosophy of Mathematics by Stephen Pollard

Author:Stephen Pollard
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Note that we are placing the non-cofinite parts of in a certain order, but we are not comparing their sizes. For example, has more entries than . Yet , since lists the smallest number that discriminates between these two lists. Indeed, the list of all odd numbers precedes even though the former has infinitely more entries than the latter.

Exercise 4.26

Show that one non-cofinite part of precedes all the others

Exercise 4.27

Show that if is a non-cofinite part of , then for some number .

Exercise 4.28

Show that if and are non-zero numbers, then .

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