Why does 24 not divide 12?

Question

If t|s just means that s = tu, for some integers t and u, then why can we not say that 24|12, since 12 = 24(1/2)? Is there some additional part to the definition I am missing?

Answer 1

Your definition is correct, however, $\frac{1}{2}$ is not an integer. Indeed, we can say that $12\mid 24$ since $24=12(2)$ because $2$ is an integer.