# When to use equal to or equivalent to?

1. ### Darth Frodo

209
When is it appropriate to use $\equiv$ as opposed to =?

2. ### phinds

8,342
well, here are a couple of examples, although I don't know that it would ever be wrong to use = when you mean equivalent.

y = ax + b [this is an "assignment" which is typical for "="]

a + b == b + a [this is not an assignment but a statement of equivalence]

### Staff: Mentor

Use ##\equiv## for equations that are identically true, such as (x + 1)2 ##\equiv## x2 + 2x + 1 and sin2(x) + cos2(x) ##\equiv## 1. Each of these equations is true for any real x.

Use = for equations that are conditionally true, such as 2x + 1 = 5. This equation is true only for x = 2; i.e., only under certain conditions.

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4. ### Darth Frodo

209
Oh ok. Thanks Mark & phinds! That really cleared it up!