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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 $(f(x))^2$.
Apr 9, 2014 · 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.
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.
AMBIGUOUS PEMDAS. OLIVER KNILL. Abstract. A source collection about the mathematical syntax in the ring Z. 1. Pemdas. 1.1. In the commutative additive group (Z; +; 0) one usually writes x for the inverse element. One has then x + ( x) = 0 or x x = 0 for short.
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Mechanically, the people on the "9" side – such as in the mostpopular YouTube video onthis question – tend to calculate 6÷2(1+2)=6÷2×3=3×3=9, or perhaps they write it as 6÷2(1+2)=6÷2(3)=3(3)=9. People on this side tend to say that a(b) can be replaced with a×bat any time. It can be reduced down to that: the teaching that"a(b) is always interchangea...
It's a fact that Google, Wolfram, and many pocket calculators give the answer of 9.Calculators' answers here are of course determined by their input methods. Calculators obviously aren't the best judges for the PEMDAS Paradox. They simplyreflect the current disagreement on the problem: calculator programmers are largely aware ofthis exact problem a...
It should be pointed out that conventions don't need to be unified. If two of my studentsargued over whether the least natural number is 0 or 1, I wouldn’t call either of them wrong, norwould I take issue with the lack of worldwide consensus on the matter. Wolfram knowstheconvention is split between two answers, and life goes on. If everyone who ca...
David Linkletteris a graduate student working on a PhD in Pure Mathematics at the University of Nevada, Las Vegas, in the USA. His research is in set theory - large cardinals. He also teaches undergraduate classes at UNLV; his favourite class to teach is Discrete Maths.
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.
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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”
