Is it allowed to use "equal to" and "approximately equal to" in the same sentence?

Question

Let's use the following example:

$$17! = 16!*17 \approx 2 \cdot 10^{13} * 17 = 3.4 \cdot 10^{14} $$

Are you allowed to do this? I am in doubt whether or not this indicates that $17! = 3.4 \cdot 10^{14}$, which is obviously not true, but I think it doesn't.

Answer 1

Your example claims that two things are equal (on the left), two things are equal (on the right), and that the left pair are approximately equal to the right pair.

One should be careful with too much use of the ill-defined $\approx$ symbol, or you can get $$1\approx 1.01\approx 1.02\approx \cdots \approx 1.99\approx 2$$

Answer 2

It is allowed. It is like asking: does $$10 = 5*2 \geq 5$$ indicate that $10=5$?