I searched for the definition of "quotient" and I felt there were many answers. Is there a place that defines math terms? Something like a standard?
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I'm afraid the answer is: no, there is no such standard. – Wojowu Dec 20 '15 at 10:06
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There are quite a few things associated with the word quotient: https://en.wikipedia.org/wiki/Quotient_(disambiguation) – Element118 Dec 20 '15 at 10:07
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You can see ISO 31-11 : "about mathematical signs and symbols, their meanings, verbal equivalents and applications". – Mauro ALLEGRANZA Dec 20 '15 at 10:08
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No, there is no canonical dictionary of mathematical terminology nor should there be.
The important thing is context. For example, to the average person quotient means something like $\frac{a}{b}$. To an algebraist there are things called quotient groups.
Mathematical terminology is always changing. A "number" a few thousand years ago might have only meant $1,2,3,...$ where now we have much broader ideas about what constitutes a number.
To answer your question more practically, just use textbooks or Wikipedia.