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Dec 24, 2012 · Abuse of notation is tolerated when the alternative is worse! In some cases, abuse of notation isn't really abuse at all, but simply a lack of fleshing things out. For example, I'm sure many would consider. arctan(+ ∞) = π / 2. an abuse of notation that is meant as shorthand for. lim x → + ∞arctan(x) = π / 2.
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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.
Abuse of notation should be contrasted with misuse of notation, which does not have the presentational benefits of the former and should be avoided (such as the misuse of constants of integration [1]). A related concept is abuse of language or abuse of terminology, where a term — rather than a notation — is misused. Abuse of language is an ...
For example, when a physicist says "delta function" and a mathematician answers "it is not a function", there is no referee to decide which is right. – GEdgar. Feb 3, 2019 at 13:34. 6. Not an answer: 1) Abusing notation often helps understanding at an advanced level. 2) There is much more abuse of notation than you may be aware of, even in ...
11.6.1 The Mating Ritual. The procedure for finding a stable matching can be described in a memorable way as a Mating Ritual that takes place over several days. The following events happen each day: Morning: Each man stands under the balcony of top choice among the women on his list, and he serenades her.
Sep 2, 2015 · abuse of equal signs. I am referring to questions like THIS. Expressions like "3 = 6" are an abuse of notation and, as such, make doing mathematics correctly harder instead of easier. Mathematics is peppered with mathematicians abusing notation, often justifying their actions by saying that "the context" should make what they mean clear.
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Abuse of notation. 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). However, since the concept of formal/syntactical ...
