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Topic: Just what is equality in mathematics, anyway?
Replies: 45   Last Post: Apr 20, 2012 5:56 PM

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 Paul A. Tanner III Posts: 5,920 Registered: 12/6/04
Re: Just what is equality in mathematics, anyway?
Posted: Apr 17, 2012 11:32 AM

On Mon, Apr 16, 2012 at 10:00 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>I don't think "identify" means what you think it does.
>
> Identify means isomorphism in this case.

Isomorphism is an equivalence relation.

> Even natural isomorphism, and Paul thinks naively that means equality in all possible contexts forever amen.
>

No. I repeat what I said in

http://mathforum.org/kb/message.jspa?messageID=7769907

which is:

"In all of my posts in this thread, let "equivalence" be an equivalence relation (a relation that is under the reflexive, transitive, and symmetric properties) and let "equality" be an equivalence relation that also is under the antisymmetric property"

I also in

http://mathforum.org/kb/message.jspa?messageID=7769907

said:

"I am taking Rudin to say that complex (a,0) and real a are equivalent, and using his Theorem 1.29 in whose proof he uses this equivalence via the replacement property, to derive the equality of complex (a,0) and real a."

You need to stop telling falsities about what I write.