- #1

DaveC426913

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: equals sign with a squiggle (tilde) over it

Do these both mean exactly the same thing?

Do they both mean 'approximately equal to'?

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- #1

DaveC426913

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: equals sign with a squiggle (tilde) over it

Do these both mean exactly the same thing?

Do they both mean 'approximately equal to'?

- #2

matt grime

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no

[tex]\cong[/tex]

means isomorphic, certainly not approximately equal

[tex]\cong[/tex]

means isomorphic, certainly not approximately equal

- #3

DaveC426913

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What does isomorphic mean?

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DaveC426913

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What about a double squiggle?

Is the equals sign with a squiggle (tilde) over it not appropriate even for a grade school textbook?

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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 said:

What about a double squiggle?

Is the equals sign with a squiggle (tilde) over it not appropriate even for a grade school textbook?

- #6

DaveC426913

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OK, I've got some context now:

They use both equal-with-squiggle and double-squiggle in the above.

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jcsd

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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.

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Galileo

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- #9

matt grime

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[tex] \simeq[/tex]

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.

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DaveC426913

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

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.

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.

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Daniel.

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jcsd

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single squiggle means "is on the order of magnitude of" or "is on the order of"

...if i am right...

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saltydog

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If the series of functions:

[tex]\sum_{n=1}^{\infty}c_nf_n(x)[/tex]

converges point wise (or uniformly) to f(x), we say:

[tex]f(x)=\sum_{n=1}^{\infty}c_nf_n(x)[/tex]

If the series converges in the mean to f(x), we say:

[tex]f(x)\doteq\sum_{n=1}^{\infty}c_nf_n(x)[/tex]

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

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