When to use equal to or equivalent to?

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SUMMARY

The discussion clarifies the appropriate use of the symbols "=" and "\equiv" in mathematical expressions. The symbol "=" is used for equations that are conditionally true, such as "2x + 1 = 5," which holds true only for specific values of x. In contrast, "\equiv" is reserved for identities that are universally true, such as "(x + 1)² \equiv x² + 2x + 1" and "sin²(x) + cos²(x) \equiv 1," which are valid for all real numbers x. Understanding these distinctions enhances mathematical precision and clarity.

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Darth Frodo
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When is it appropriate to use \equiv as opposed to =?
 
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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]
 
Darth Frodo said:
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.
 
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Oh ok. Thanks Mark & phinds! That really cleared it up!
 

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