When to use equal to or equivalent to?

[Darth Frodo]

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

 

[phinds]

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]

 

[Mark44]

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

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.

 

[Darth Frodo]

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