What Do Different Symbols Over an Equals Sign Mean?

[DaveC426913]

: 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'?

 

[matt grime]

no

$$\cong$$
means isomorphic, certainly not approximately equal

 

[DaveC426913]

What does isomorphic mean?

 

[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?

 

[hypermorphism]

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.

 

[DaveC426913]

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.

 

[jcsd]

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.

 

[Galileo]

A professor of mine once said: "The squiggly sign is an astronomers favourite tool. They only have to get an order of magnitude anyway."

 

[matt grime]

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.

 

[DaveC426913]

This PDF http://www.fsz.uni-hannover.de/Sprachbereiche/Englisch/dozenten/mcelholm/download/maths_02.pdf
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.

 

[dextercioby]

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.

 

[jcsd]

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.

 

[phyility]

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...

 

[saltydog]

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:

$$f(x)\doteq\sum_{n=1}^{\infty}c_nf_n(x)$$

 

[gazzo]

I've always wondered, what about the equals sign with a triangle over it?