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1. math.stackexchange.com › questions › 1024280Most ambiguous and inconsistent phrases and notations in maths

   math.stackexchange.com › questions › 1024280

   Nov 18, 2014 · What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a function $f$: $f^{-1}(x)$ can be an inverse and a preimage and sometimes even $\frac{1}{f(x)}$. $f^2(x)$ can be $(f\circ f)(x)$ and $(f(x))^2$.

2. nrich.maths.org › articles › numbers-and-notationNumbers and Notation - Ambiguities and Confusions - NRICH

   nrich.maths.org › articles › numbers-and-notation

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   Some occur only in rather specialised situations, but many are fundamental and part of everyday experience. Here are some items from my collection - reactions and further examples will be appreciated.

3. people.math.harvard.edu › ambiguity › indexAmbiguous PEMDAS - Harvard University

   people.math.harvard.edu › ambiguity › index

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   Apr 9, 2014 · Some of the most popular videos are ambiguous expressions involving the order of operations. In doing research, I came across your website and the problem: What is 2x/3y - 1 if x = 9 and y = 2? I would answer 11, which was what the 5th grade teacher said.

4. davidwees.com › ambiguity-mathematical-notationAmbiguity in mathematical notation – The Reflective Educator

   davidwees.com › ambiguity-mathematical-notation

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   Jul 9, 2013 · Off the top of my head, two examples of notation that often confuse some students: Inverse trig function notation sin^(-1)(x)≠(sin x)^(-1) even though sin^2(x)=(sin x)^2. Function notation in general: sin(x) confused with “sin” times “x”

5. math.stackexchange.com › questions › 2505777Abusing mathematical notation, are these examples of abuse?

   math.stackexchange.com › questions › 2505777

   Nov 5, 2017 · The example you've given of a function is not an abuse. x is instead shorthand for π1(t) and y is shorthand for π2(t) and (x, y) is shorthand for t. g ∈ G is a very minor abuse, yes. "A group G is a set G endowed with some operations" is a slight abuse, but one which will never be misinterpreted.

6. math.stackexchange.com › questions › 1102156Why does notation for functions seem to be abused and ambiguous?

   math.stackexchange.com › questions › 1102156

   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.

7. People also ask

   What are some examples of ambiguous notations and words in maths?

   • What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a function f: f − 1(x) can be an inverse and a preimage and sometimes even 1 f (x). f2(x) can be (f ∘ f)(x) and (f(x))2.

   Most ambiguous and inconsistent phrases and notations in maths

   math.stackexchange.com/questions/1024280/most-ambiguous-and-inconsistent-phrases-and-notations-in-maths

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   What is ambiguity in notation?

   • That is the definition. This is not where the ambiguity is. It is that the notation is ambiguous (and experience shows that that it is a source for errors and misunderstandings). For example, if we write x/3x, then many humans understand the result as x/ (3x) which is 1/3. If you give it to a machine, then it gives the result x/3x =x^2/3.

   Ambiguous PEMDAS - Harvard University

   people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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   What is an example of an ambiguous problem?

   • The classic example is 8/2 (2+2) which could be read as either (8/2) (2+2) or 8/ (2 (2+2)). I see people reference your write up to support that this problem specifically is ambiguous. You go on to offer a few more examples such as 2^2^2 as ambiguous.

   Ambiguous PEMDAS - Harvard University

   people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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   Does math always have ambiguities?

   • One forgets that language always had and always will have ambiguities. It is a social construct and so can not be engineered easily. You say: "I think that math is not confused, only we are confused". Math has never been confused. But math is also a language that must be spoken and is used to communicate ideas.

   Ambiguous PEMDAS - Harvard University

   people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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   What is a non ambiguous expression?

   • Non-ambiguous expressions either use brackets like 8/ (2 (2+2)) An other possibility is to use the expression 8 ---------------- 2 (2+2) This gives 1. In that it is important that there is a clear long fraction division line making sure that the 2 (2+2) is done before the division.

   Ambiguous PEMDAS - Harvard University

   people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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   How do you answer ambiguous equations?

   • Similar to 1, for expressions/equations presented ambiguously, require students to indicate by the use of parentheses etc. how they went about solving the expression. In this case, the right answer depends on how the student organizes the equation.

   Ambiguous PEMDAS - Harvard University

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8. www.people.vcu.edu › ~rhammack › Math490Mathematical Writing - Virginia Commonwealth University

   www.people.vcu.edu › ~rhammack › Math490

   Since x and X can have entirely di erent meanings, putting such symbols at the beginning of a sentence can lead to ambiguity. Following are some examples of bad usage (marked with ) and p good usage (marked with ). is a subset of B. The set A is a subset of B. is an integer, so 2x + 5 is an integer. Since x is an integer, 2x + 5 is an integer.