2000 | Cardinality, Counting and Equinumerosity |
3 | p.194 | 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) |
3 | p.196 | 17449 | We can understand cardinality without the idea of one-one correspondence |
4 | p.198 | 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence |
4 | p.199 | 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers |
5 | p.200 | 17453 | The meaning of a number isn't just the numerals leading up to it |
5 | p.200 | 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set |
5 | p.201 | 17454 | Children can use numbers, without a concept of them as countable objects |
5 | p.202 | 17455 | Is counting basically mindless, and independent of the cardinality involved? |
5 | p.202 | 17456 | Counting is the assignment of successively larger cardinal numbers to collections |
6 | p.202 | 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity |
6 | p.203 | 17458 | Equinumerosity is not the same concept as one-one correspondence |
6 | p.204 | 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms |