Mathematical English
Mathematical English is not the same as standard English!
The assumption that it is causes a lot of confusion. For
example, the words function
, group
,
and integral
have completely different meanings, and if
you expect their meanings to relate to the normal English
meanings of these words in any sensible way you will be sorely
misled.
In standard English, words have:
- Many denotations, determined by usage
- Many connotations, determined by usage
In mathematical English, on the other hand, words have:
- One denotation, determined by fiat. In other words, whoever is writing the text or giving the lecture just decides what words mean, perhaps in a completely arbitrary way, and everyone discussing the text or the lecture simply agrees to go along with it.
- Zero connotations