## Sunday, February 07, 2016

### Super Bowl 50

(Click on the comic if you can't see the full image.)

Let the discussion of Ordinal v. Cardinal begin now.

Seriously, I get comments from people who get it backward and/or think I got it backward.

As for our buddy, L in the comic, he is refering to last year's comic.

Come back often for more funny math and geeky comics.

xKiv said...

Hm. I am aware of two different definitions of ordinaL vs. cardinal numbers:

In number theory, the way I was taught it - we may have had a very constructionist approach:
Ordinals start with zero (the empty set), and you can get new ordinals either by adding one (N+1 is the set {0,1,...,N} which has exactly N+1 elements for finite N), or by taking the transfinite step (which basically takes a set of ordinals for which "add one" no longer does anything, and generates a "next larger" ordinal; we constructed it as taking the union of all ordinals in the given set); they are well-ordered (it's always possible to pick a least element out of any set of ordinals - it's their intersection).
Cardinals are a special case of ordinals. An ordinal A is called cardinal if there is no ordinal B such that B is strict subset of A (B is "smaller" than A) and there is bijection between A and B.
In this sense, every cardinal is an ordinal, most (infinite) ordinals are *not* cardinals, and all finite numbers (like 50) are both.

In grammar:
Ordinal numbers are words denoting order, like "first, second, third, ..., 50th, ..."
Cardinal numbers are words denoting amount, like "one, two, ..., 50, ...".
In this sense, neither can be the other, and 50 is only cardinal.

I also note that grammar and number theory don't mix. Grammar is about words, number theory is about some abstract entities (that may be refered to by words, but are not the words).

I also also note that neither of them talk about ordinaRY numbers. What are those?

(x, why?) said...

Taking the bait for the sake of conversation,

If you have anthropomorphic numbers talking, one can insult the other be called them "ordinary". And this comic uses bad puns all the time, so using ordinary as an adjective isn't anything new.

For that matter, growing up with a Church calander which denoted things like "the Fifth Sunday in Ordinary Time" contributes to use of that adjective.

Enjoy the game.