Don't do that.
Infinity is not a number! The "cancelling infinity" so-called-trick often does not work on limits where l'Hospital's rule applies (e.g. , rewritten in
form). And on functions f where "
" is undefined. Well, ok, strictly speaking it never really is defined, unless we resort to weirdness like the extended real line, but if
or something, then even an extended real number line won't save you.
I suppose now would also be a good time to make "snarky" remarks about chemical engineers and their (lack of) mathematical rigor, even if they have a PhD.
Side remark: Yes, I read the archives of random blogs when I am procrastinating. Funny what lengths can one go in trying to avoid studying physics.
Monday, April 21, 2008
A Post That Makes Me Cringe
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1 comment:
that's an interesting question: how much abstract math are you supposed to use
for example I argued with a physical chemistry post doc if you are allowed to divide a differential by dV or if you are actually doing a differentiation with the chain rule, I did not like how he did it but it was the same result
or: are you allowed to write things like dx = t dt for substitution in integration?
about the polynomial division: if you put it differently it's ok. you can say that the net (or sequence) (2x+1)/x gets arbitrarily close to 2x/x. and the limit 2x/x=2 is of course 2. and if the difference between two nets approaches 0 they have the same limit
by the way: when you say infinity is not a number, you have to clarify what a number is. infinity can not be an element of a field. but if you say that a number is an element of a metric space, then it works. because you can have metrics that include infinity
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