Frequently in my math and physics classes I see teachers use the equivalence sign (an equal sign with an extra dash) seemingly interchangeably with the equal sign = .
I haven’t been able to discern what the rule is for when you use one or the other, except that one teacher said that when you have different units that represent the same amount, for example, 100 cm (equivalent to) 1 m. Is this true. What are the rules for using these symbols?
IIRC, “=” is “equal” while “≡” is “identically equal.” I think the latter is used when the equation holds true for all values of its variables. For exampe:
x^2 - 4 ≡ (x - 2) (x + 2), because it is true for all values of x
x - 2 = 5, because it is only true when x is 7
When representing conversions, it seems like you should use the equivalence sign (since “1 m” will always be equal to “100 cm”) but you probably won’t be lynched for using the plain old equals sign.
Thanks. One other thing. How do you make the equivalent sign on the computer?
If you’re using LaTeX, you make the equivalence sign by using the \equiv command while in math mode. If you’re not using LaTeX, you should be using LaTeX.
What’s LaTeX?
I agree. You can read more about LaTeX here, or you can Google it (it’s generally safe). MiKTeX is an excellent Windows-based implementation, if it’s something you find interesting.
In Windows, to make the symbol outside of LaTeX, you can use the Character Map. Go to Program Files->Accessories->System Tools->Character Map. Look under the Arial font (although it should show up in several fonts), and it’ll be in the last quarter - just below all of the A’s and e’s. Double-click it, hit the Copy button, and paste it into whatever you want.
If you need to know special characters, IMHO, much easier than reading a character map is to go to:
http://www.1728.com/altchar.htm
Unfortunately, the equivalence symbol ≡ is found in Section 2 of that page - meaning it is not 100% reliable to be displayed properly in all situations.
Anyway, hold down the “ALT” key and at the same time type 240 on the keypad and you should get the ≡
The most frequent use of the “equivalence” sign is in defining a quantity. I also had a professor who would write an equals sign with a little triangle over it in definitions. I find the distinction between = and “equivalence” very useful conceptually. F=ma and T=1/2 mv[sup]2[/sup] both use the equals sign, but the sign means completely different things. I would write T (equivalence) 1/2 mv[sup]2[/sup] .
Hm… I was going to suggest an underlined equals sign:
=
but I guess not.
[hijack]
I thought (mv[sup]2[/sup])/2 was the formula for kinetic energy. Why’d you use a T, Hyperelastic?
The equivalence sign ‘≡’ seems to be used in two subtly different ways.
One way means something like “by definition”. So if you see something like A ≡ B[sup]2[/sup]C (a made up example), it means that the symbol A is nothing other than an abbreviated way of denoting the expression B[sup]2[/sup]C. Whereas, if an equality sign ‘=’ is used, A and B[sup]2[/sup]C might represent two different concepts which could, in principle, yield two different quantities.
The second way that ‘≡’ is used was described by jmizzou. You might write ƒ(x) ≡ 0 instead of ƒ(x) = 0 to indicate that equality holds for all values of x, not just for some particular value. So “ƒ(x) ≡ 0” can be thought of as just shorthand for “ƒ(x) = 0 for all values of x.”
The rules are whatever you define them to be when you’re laying out your formalism and notation. That’s it.
Yeah, but these people are physicists. They never do that ;).