# Cardinal numbers? HELP!

HELP!

Somewhere I learned or thought I learned about cardinal numbers.

Example: the engine of a auto mobile is the number one part on a car.

Example: to love God, self and neighbor is the cardinal or number one commandment.

Cardinal and not ordinal.

I cannot recall where I learned this, not if I recall properly.

Also, but side note: can we have qualitative numbers instead of merely quantitative numbers?

I believe we can!

THANKS!

I think you are thinking about two different meanings of cardinal.

A cardinal number is something that indicates quantity (i.e. five cars) as opposed to ordinal numbers which indicate position (i.e. the car in 5th position).

The use of cardinal in your examples are not about numbers per se, but rather the primacy of a thing (i.e. cardinal virtue). Similar concepts, but not really the same thing.

Cardinal refers to countingnumbers, 1,2,3,4…

Ordinal refers to order 1st, 2nd, 3rd…

Green tree frogs.

A cardinal number is a counting number such as: 0,1,2,3,4,…
Two sets have the same cardinality if there is a one-to-one and onto correspondence (bijection) between them. The cardinality of the real numbers is greater than that of the natural numbers. No one knows if there is a set of numbers with cardinality less than that of the real numbers, but greater than that of the natural numbers. There is a mathematician who believes the problem can be solved in a multiverse.

Who? Pray tell.

Joel David Hamkins
“In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for.”
arxiv.org/pdf/1108.4223v1.pdf
arxiv.org/abs/1108.4223
arxiv.org/abs/1104.4450
arxiv.org/abs/1108.4223

Thank you!

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