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[Merged by Bors] - feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat-valued cardinalities #6494

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[Merged by Bors] - feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat-valued cardinalities #6494

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Defines cardinal.to_nat and cardinal.to_enat
Uses those to define nat.card and enat.card

@awainverse awainverse added the awaiting-review The author would like community review of the PR label Mar 1, 2021
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nat.card should be equivalent to the frequently-discussed fincard.
I have also included enat versions, because while nats are usually more convenient, cardinal.to_enat is better-behaved, as it is an additive homomorphism. If we define multiplication on enats such that 0 * top = 0, then it will also be a multiplicative homomorphism. (I assume that'd constitute a semiring homorphism, but I haven't checked that that would actually make enat a semiring).

@Vierkantor Vierkantor mentioned this pull request Mar 4, 2021
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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Mar 4, 2021
bors bot pushed a commit that referenced this pull request Mar 4, 2021
@awainverse
feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat…
1cc59b9 
…-valued cardinalities (#6494)

Defines `cardinal.to_nat` and `cardinal.to_enat`
Uses those to define `nat.card` and `enat.card`
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bors bot commented Mar 4, 2021

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat-valued cardinalities [Merged by Bors] - feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat-valued cardinalities Mar 4, 2021
@bors bors bot closed this Mar 4, 2021
@bors bors bot deleted the cardinal_to_nat branch March 4, 2021 17:49
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
@awainverse @b-mehta
feat(set_theory/cardinal, data/nat/fincard): Define nat- and enat…
f97b641 
…-valued cardinalities (#6494)

Defines `cardinal.to_nat` and `cardinal.to_enat`
Uses those to define `nat.card` and `enat.card`
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@jcommelin jcommelin jcommelin approved these changes

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