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The 'triple' equals

No doubt it has a proper name but the equals (=) with 3 lines instead of 2 is what I am curious about. What does it mean? and when do I use it? :confused:

Reply 1

oliviaj28

It's an identity symbol, and means that both sides of the equation are always true. For example a/2 = 0.5 x a, and this is true for any possible value of a.

Hope this helps :-)

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Reply 2

rayquaza17

Original post by Substitution

No doubt it has a proper name but the equals (=) with 3 lines instead of 2 is what I am curious about. What does it mean? and when do I use it? :confused:

Congruent to.

Or identical to for ALL values.

Eg: Sin^2(x) + Cos^2(x) = 1 for ALL values of x.

Reply 3

Substitution

Original post by rayquaza17

Congruent to.

Or identical to for ALL values.

Eg: Sin^2(x) + Cos^2(x) = 1 for ALL values of x.

When simplifying eqns would I be able to use it? e.g. (2/x)-(1/x)==(1/x)?

Reply 4

yo radical one

As others have said it's the identity symbol

e.g.

1 + 1 = 2

a + b ≡b + a (where a and b are real numbers)

Reply 5

interstitial

Original post by Substitution

When simplifying eqns would I be able to use it? e.g. (2/x)-(1/x)==(1/x)?

Yes, if you are algebraically rearranging you can, but this 'identity' would not be true for x=0 so you cannot use it here.

I believe it's known as the equivalence symbol (at least in LaTeX) and the congruence symbol when referring to shapes.

You normally use the implies sign

\implies

or the regular equals sign when rearranging.

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(edited 10 years ago)

Reply 6

rayquaza17

Original post by Substitution

When simplifying eqns would I be able to use it? e.g. (2/x)-(1/x)==(1/x)?

I suppose so, but you wouldn't really do that. It's best just to stick to a normal equals sign.

It's like how people write "don't" instead of "do not" - you could write it either way, but one way is more common.

Edit: As someone says above, it's not true for x=0. I thought there was a value it didn't work at, but I couldn't put my finger on it! (It's been a long 3 month term...)

(edited 10 years ago)

Reply 7

Smaug123

Original post by Substitution

No doubt it has a proper name but the equals (=) with 3 lines instead of 2 is what I am curious about. What does it mean? and when do I use it? :confused:

It's also used in modular arithmetic, by the way, although IIRC it's not covered at A-level.

Reply 8

miser

Triple equals denotes identity, i.e., that two sides of the operand are not only equal, but their meaning is identical. As noted in the post above me, it's used in modular arithmetic, e.g. 0 ≡ 5 mod 5, since 5 mod 5 is identical to 0. In programming languages it also indicates identity where equality can be ambiguous. For example, in PHP, 0 == false. However, it is not the case that 0 === false, because although they are considered to be equal, their data types are not the same and thusly are not identical.

Reply 9

natninja

Original post by Substitution

No doubt it has a proper name but the equals (=) with 3 lines instead of 2 is what I am curious about. What does it mean? and when do I use it? :confused:

I've seen it used as 'is defined as'

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