Implementation of mathematics in set theory: Difference between revisions

Revision as of 19:08, 21 December 2005

Revision as of 19:09, 21 December 2005

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can write this <math>|A|=|B|</math> as long as we note that for the moment this expresses

a relation between A and B rather than a relation between objects <math>|A|</math> and

<math>|B|</math> which have not yet been defined. We also provide notation <math>A \sim B</math>

for this notation to be used in contexts such as the actual definition of the cardinals where

even the appearance of presupposing abstract cardinals should be avoided.

Similarly, we can define <math>|A| \leq |B|</math> as holding iff there is an injection