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.

]]>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

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.

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