Re: Explanations

[peasthope@shaw.ca]

Charles & everyone,

Earlier peasthope wrote,
"...changing a few words of a sentence can make a concept obvious rather
than nebulous".  Revise that to "obvious rather than difficult".

From:	Charles Wells <charles@abstractmath.org>
Date:	Fri, 22 Apr 2011 09:37:44 -0500
> Can you give specific examples?  I suspect that in most cases the change
> introduces a useful metaphor that was hidden before.

Here is a small example from the _Conceptual Mathematics_ of
Lawvere and Schanuel.  No offense to the authors or the book.
It's an indispensible and invaluable resource.

L&S page 292, "Definition ... equalizer ... and for each x:T-->X ... there is
exactly one e:T-->E ... ."    "For all T" is implicit.

http://en.wikipedia.org/wiki/Equalizer_(Mathematics) , "In category theory
... defined by a universal property, ... object E and morphism eq ... such that,
given any other object O and morphism m ... ."

For me, the reference to "any other object O" helps.  The definition in the
Wikipedia seems to reveal the "universality" of the equalizer better.  The
diagram also helps.

A trivial issue for most readers but a small detail can make a difference for
a student.

Regards,                     ... Peter E.

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