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In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time).
Dec 24, 2012 · In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not formally correct but that seems likely to simplify the exposition or suggest the correct intuition (while being unlikely to introduce errors or cause confusion).
- Definition
- Examples
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Mathematical notation can be considered in two ways: 1. As an aid to mathematical understanding, no more and no less than a useful convention to encapsulate more or less complicated ideas in a completely unambiguous format; 1. As the reason for mathematical effort, so as to encapsulate a truth as a documented piece of aesthetic beauty in its own ri...
Correct Use of Logarithms
Using this mnemonically useful identity: 1. logablogbc=logaclogablogbc=logac rather than the less easy to remember: 1. logbc=logaclogablogbc=logaclogab is likely to get you banned from the teaching profession in certain of the less liberal realms of the Western hemisphere. You are, apparently, supposed to remember (and teach, and cause to be remembered) the second of these identities, as it indicates directly what it is for. That is, its purpose is to allow you to convert from logarithm...
Non-perpendicular Coordinate Axes
When one is constructing a pair of coordinate axes, it is possible to set them up at an angle different from 9090degrees from each other. In particular, when investigating symmetries of patterns and friezes based on the geometry of the equilateral triangle, it can be convenient to set up a pair of axes at 6060degrees to each other. If you are tempted to do so, then according to the aesthetic school, you may not call them xx and yy. Those terms are reserved for a pair of axes which are strictl...
Differentials
It is convenient, in many situations, to treat derivativesas fractions even though, strictly speaking, they are not. For example: Thinking about why this sort of manipulation may or may not be justified is usually discouraged.
Ignoring these strictures can ensure that you spend the rest of your mathematical career editing websites under a carefully guarded pseudonym. Be careful your alias is not uncovered, or a lengthy prison sentence awaits.
Jan 13, 2015 · Short answer based on my opinions: (1) people don't learn grammar, (2) notation (e.g. lambda abstraction) for expressing things both precisely and conveniently is unfamiliar, and (3) people don't properly learn about dependent variables, and are instead trained to interpret everything as functions. – user14972.
Nov 5, 2017 · Yes, this is an abuse of notation, but the term "abuse of notation" in mathematical English does not carry the negative connotation that "abuse" does in non-mathematical English. Halmos's Naive Set Theory also has a passage relevant to this second example (p. 55):
f (x) is the result of applying the function f to an object x. I think that by far the most common form of abuse of notation is conflating a structure with its underlying set. If you have a group G, for instance, you'll write x ∈ G to mean that x is an element of the underlying set of G.
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In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time).
