Do any of you out there use ≡ for “identity”?  In your own work?  With little kids?

I am considering introducing it to 9th grade algebra students.

They think symbols are cool.

I know they get confused when solving  4(1-2b) = 2(3-b) – 2 , maybe the special symbol would help?

What do you think?

1. November 2, 2011 am30 6:51 am 6:51 am

I had a couple teachers in High School who would use it…none of them Math teachers. My chemistry teacher was the one that taught it to me.

That being said, when I finally got to college, I saw “” used far more frequently particularly in proofs classes and in situations of equivalence for other classes…and so out of habit, I tend to use that one. The only time I saw the one you are describing was in reference to equivalence relations modulo n in group theory.

I’m not sure if my experience is normal; but, since it is short hand, it will vary slightly from professor to professor and teacher to teacher and book to book.

Giving them exposure sure couldn’t hurt, though. I say do it.

• November 2, 2011 am30 6:59 am 6:59 am

Sorry…it seems that the comments tried to turn it into an html tag…

The trend I noticed was to use double tailed arrows like this “==>” (single tailed arrows are used exclusively for logical implications).

The equivalence would just be a double tailed arrow with two arrow heads on each side.

Also, now that I’m thinking about it further…I believe I remember hearing that the three barred equal sign meaning “is defined as” where as “= =” like you might see in a programming language for a logical test is “equivalent to.”

November 2, 2011 am30 8:01 am 8:01 am

FWIW, I’ve successfully used == in this context. 9th graders seem to like to think they are using stuff computer programmers use. For the rare sophisticated class I do a side bar about logic testing in if() statements and add other standard symbols such as >=, <=, .

November 2, 2011 am30 8:24 am 8:24 am

If := is assignment, how about :=: for “having been assigned as”?

4. November 2, 2011 am30 10:54 am 10:54 am

The only time I would use the identity symbol is with trig. identities to differentiate between identities and equations.