I have started to learn discrete maths on my own, and while writing my first proofs, I am sometimes drawn to use the verb "yield" (e.g. Let $a=2b²+5b+4$ for some integer b. Since $\Bbb Z$ is closed under addition and multiplication, a will yield an integer).
Is it OK, plain wrong, bad form? Thanks!
$\endgroup$ 12 Answers
$\begingroup$I agree with the first answer, I think 'yields' is over the top here and it is always good to write mathematics in the simplest possible way.
'Yields' is much more appropriate for when we are applying some sort of process or operation to something in order to change it into another form, an example would be 'applying the fourier transform yields the frequency domain form of our function'.
$\endgroup$ $\begingroup$I would say in your particular case, it's odd to use yield since you can simply say $a$ will be an integer. I would say
since $\mathbb Z$ is closed under addition and multiplication, $a$ is also an integer.
I would reserve the verb yield to functions, so for example, if you have $f(x)=x^2$, you could say
Since $\mathbb Z$ is closed under multiplication, the function $f$ yields an integer with integer input.
and even that is slightly weird. I honestly can't think of any use of yield that can't be improved and simplified by using the verb be.
Thanks to Erick Wong, I can now provide an example of a good use of the verb yield where you cannot replace it with be. It's when you would want to say "results in", like when you are simplifying or differentiating or doing some other thing to an equation. For example, you can say
$\endgroup$ 2Simplifying the equation $a^2 + b^2 + 2c^2 = r^2 + c^2$ yields $a^2+b^2+c^2=r^2$
