hi Al-Allo

In your example you could drop the word altogether and have "The only restriction is that the divisor must not be equal to zero" and it still makes perfect sense. I've been trying to find situations where just using 'equals' is not appropriate ... without much success I have to say.

Some mathematicians use 'identically equal' instead of 'equivalent' and it is often used for identities eg.

and also eg.

If you google the two word phrase you'll get more examples.

Meanwhile, here's a challenge for members:

Find an example where you cannot leave out the word 'identically' without changing the meaning.

Bob