Re: Opinions on mathematics.

"Nathan" <ntspam2@xxxxxxxxxxxx> writes:

Bob Kolker wrote:
How about the cardinal number 2. That is the class
of all sets which are equinumerous with {a, b}.

So 2 is a *proper class*? No way! Finite cardinals are finite sets.
2 = {0,1} = {0,{0}}, where 0 is the empty set.

Bob is referring to an updated version of Frege's definition of
cardinal numbers.

You are referring to von Neumann's definition. There are also other
definitions. Why pretend that the cardinals can only be defined in
this and no other way?

--
"[In the movie, Tom Green] delivers a child, severs the umbilicus with
his teeth and then swings the baby over his head before tenderly
handing it to the stunned, blood-spattered mother[...] This was, I
have to say, a bit much." -- New York Times movie reviewer A. O. Scott
.

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