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.

If I were to write $3 < 3+1 = 4$, would you deduce that $3=4$? — lokodiz, Oct 05 '14 at 15:39
It's fine. $a=b\approx c=d$ means that $a=b, b\approx c, $ and $c=d$. It does not mean that $a=d$. — MJD, Oct 05 '14 at 15:45

score 3 · Accepted Answer · answered Oct 05 '14 at 15:37

3

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 $$1\approx 1.01\approx 1.02\approx \cdots \approx 1.99\approx 2$$

answered Oct 05 '14 at 15:37

vadim123

82,796

3

And all those claims are correct. – Ross Millikan Oct 05 '14 at 15:39
I disagree. It is legitimate to use it that way, just as one can write (for example) $5\cdot7=35>30=5\cdot6$. This notation is often used in more complex proofs. – barak manos Oct 05 '14 at 15:47
@barakmanos, the $>$ symbol is well-defined and transitive; with what are you disagreeing? – vadim123 Oct 05 '14 at 15:48
Sorry, I misinterpreted your answer. – barak manos Oct 05 '14 at 15:51

score 1 · Answer 2 · answered Oct 05 '14 at 15:38

1

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

answered Oct 05 '14 at 15:38

C_Guy

333

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

2 Answers2