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# The difference between :=, ≜, ≡ and =

Sometimes you see other symbols for equals and you may wonder what the difference is or why they are used since the thing on the left equals the thing on the right. Well I think that you do not need to worry about it too much because the = is often substituted for the others but it isn't strictly correct because the others symbols are saying that one thing equals another AND they are saying something additional. Not all mathematicians agree on which symbol to use either.
Here are the differences between the symbols.

## Identity

8(2 - x) ≡ 16 - 8x which is true for all values of x
 tan x ≡ sin x tan x again, this is true for all values of x
cos2 θ + sin2 θ = 1 (an itentity)

≡ means "is identical to" or "is equivalent to". This shows that one side of the symbol is an alternative form to the other. You notice that x here is on both sides. The ≡ may mean that you can use one equation or the other. You could also think of it as showing another way of writing an equation.

## Defining equation

n2 ≜ n × n
sin2 x ≜  (sin x)2

≜ means "is defined to be" so it shows what one thing means

## Assigning equation

n:=10
The := simply means that a specific value is assigned to the variable.

## Conditional equation (usually just called an equation)

n2 = 64
This just means that it is true for certain values. In this case, n = ± 8

## Formula

A = πr2

This just expresses a mathematical fact

In conclusion, you could use = for all the above if you wish.
Also some people use any one of the following symbols for "is defined by" =: := ≡ :⇔ ≜ ≝ ≐
It is not uncommon to use one symbol to mean different things for example, ≡ can be used in modulo arithmetic, 5 ≡ 2 mod 3 (which is congruence) and I have seen := used for "is defined by".

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