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## #1 2006-02-20 03:09:13

John E. Franklin
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### I don't know what ≡ means.

I don't know what ≡ means in krassi's topic.

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #2 2006-02-20 03:19:38

irspow
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### Re: I don't know what ≡ means.

I believe that it means that the term on one side is the definition of the term on the other side.  They are more than just terms that are equivelent but exactly the same.  Does that make sense?

After doing a little research I came upon;

"  x ≡ y means x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence). "

However congruence can mean as little as a similarity, so I guess that you have to determine its meaning from the context in which it is used.

Last edited by irspow (2006-02-20 04:10:17)

## #3 2006-02-20 04:28:51

Ricky
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### Re: I don't know what ≡ means.

x ≡ y out loud is "x is equivalent to y".  What does equivalent mean?  Depends on where you see it.

Two things are equivalent if they share the same property.  The one who writes it must define the property that they are talking about.

For example, if I wish to talk about even and odd integers, 2 ≡ 4 because they are both even, 3 ≡ 5 because they are both odd, but 2 <≡> 5.  (I just  made up <≡>, because <> means not equal, and it looks pretty nice).

Or we could use it in terms of names that start off with the same letter:

Ryan ≡ Robert
Mark <≡> Ben

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #4 2006-02-20 05:11:33

mathsyperson
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### Re: I don't know what ≡ means.

Yes, I learnt it as being 'identical to' too.

eg:

(x+2)² ≡ x² + 4x + 4
x+2 = 9.

You can use ≡ in the top equation because it is always true, but for the lower one you need to use = because it is only true when x = 7.

Why did the vector cross the road?
It wanted to be normal.

## #5 2006-02-21 03:30:06

kempos
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### Re: I don't know what ≡ means.

used for identities (trigonometry) to indicate that something is always true - in trigonometry true for any angle for example.