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!

 

[CellCoree]

The symbols "equal to" (=) and "equivalent to" (\equiv) have specific meanings in mathematics and science. In most cases, the symbol "=" is used to represent an exact numerical or algebraic equality, such as 2+2=4. On the other hand, the symbol "\equiv" is used to represent a broader concept of equivalence, where two expressions or quantities have the same value or meaning, but are not necessarily identical. For example, in chemistry, the equation H2O \equiv 2H + O represents the fact that water (\equiv) is composed of two hydrogen atoms and one oxygen atom, but they are not exactly the same.

In general, it is appropriate to use "=" when discussing exact numerical or algebraic equalities, while "\equiv" should be used when discussing broader concepts of equivalence. However, it ultimately depends on the context and the specific mathematical or scientific concept being discussed. It is important to use the appropriate symbol to accurately convey the intended meaning and avoid confusion.