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. -- Telephone 1 360 450 2132. bcc: peasthope at shaw.ca Shop pages http://carnot.yi.org/ accessible as long as the old drives survive. Personal pages http://members.shaw.ca/peasthope/ . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]