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?
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I think that $u$ has to be an integer. Since $t*u = s$, by definition of multiplication, the multiplier $u$ is an integer. – Toby Mak May 08 '17 at 23:45
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21/2 is not an integer. – TMM May 08 '17 at 23:46
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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.
Dave
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