# equals signs meanings

by DaveC426913
Tags: equals, meanings, signs
 P: 15,294 : equals sign with a dot over it : equals sign with a squiggle (tilde) over it Do these both mean exactly the same thing? Do they both mean 'approximately equal to'?
 HW Helper Sci Advisor P: 9,395 no $$\cong$$ means isomorphic, certainly not approximately equal
 P: 15,294 What does isomorphic mean?
P: 15,294

## equals signs meanings

I really appreciate this. I'm helping edit a textbook that's due in like, days, so time's a-crunchy.

Is the equals sign with a squiggle (tilde) over it not appropriate even for a grade school textbook?
P: 510
 Quote by DaveC426913 I really appreciate this. I'm helping edit a textbook that's due in like, days, so time's a-crunchy. What about a double squiggle? Is the equals sign with a squiggle (tilde) over it not appropriate even for a grade school textbook?
I would use the double-squiggle to denote approximately equal to (especially since the LaTeX for it is "\approx"). The equals sign with the squiggle over it is widely used for isomorphism, which is when two mathematical objects have the same structure and form (where form is denoted by some invertible morphism between the objects). A simple example would be a cube and any rotation of that cube.
 P: 15,294 OK, what about the dot over the equal? The book seems to use that interchangeably with the double squiggle. OK, I've got some context now: pi (equals approximately) 3.14 They use both equal-with-squiggle and double-squiggle in the above.
 PF Patron Sci Advisor P: 2,188 If two mathematical objects are isomorphic it means (infomrally) that there is a 'structure-preserving' bijection between the two objects.The symbol is also used for 'is isomorphic to' is also used to denote a geomertic congruence. I think the equals sign with a dot above it denotes 'is nearly equal to' The double squiggle means 'approximately equal to', this is the one you probably are after.
 HW Helper Sci Advisor P: 2,004 A professor of mine once said: "The squiggly sign is an astronomers favourite tool. They only have to get an order of magnitude anyway."
 HW Helper Sci Advisor P: 9,395 There is also the symbol of a dash with a tilde over it $$\simeq$$ that is occasionally used to mean approximately equal to. Perhaps that was the one you were describing? isomorphic means "sharing properties whilst not being actually identical". For instance the strictly positive real numbers under multiplication has the same structure as the reals under addition. If you know about exponentials and logs this is easy to show. So under the operations they are in essence the same but different.
 P: 15,294 This PDF Numbers and Mathematical Expressions in English ... lists squiggle-above-equals as 'approximately equal to'. Geez, an extensive Google search seems to be turning up a lot of disagreement on the issue. I guess the safest is to go with one the textbook has already used, the double squiggle.
 HW Helper Sci Advisor P: 11,720 I'd advise you to use this sign $\simeq$...But you're free to chose any sign,as long as U DEFINE IT,meaning that in the context there's no room for confusion... Daniel.
 PF Patron Sci Advisor P: 2,188 I'd say use the double squiggle as it's by far the most common (though using the dash with the tilde over it won't cause confusion), as for the pther two symobls (the euals sign wth the dot and the tilde over it) using them in this context can be confusing.
 P: 1 double squiggle means "is approximately equal to" single squiggle means "is on the order of magnitude of" or "is on the order of" ...if i am right...
 HW Helper Sci Advisor P: 1,593 One use of the dot over the equal sign is to distinguish mean convergence from pointwise convergence: If the series of functions: $$\sum_{n=1}^{\infty}c_nf_n(x)$$ converges point wise (or uniformly) to f(x), we say: $$f(x)=\sum_{n=1}^{\infty}c_nf_n(x)$$ If the series converges in the mean to f(x), we say: $$f(x)\doteq\sum_{n=1}^{\infty}c_nf_n(x)$$
 P: 179 I've always wondered, what about the equals sign with a triangle over it?

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