Is this another way of saying T is a set of multiples of 3 in N?
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delson133 7
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I would interpret (but I'm not a native english speaker) "a set of multiples of $3$ in $\mathbb N$ as a subset of the set $T$ which I would probably call "the natural numbers that are multiples of $3$". – Henrik supports the community Sep 16 '17 at 08:29
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What is the lower case $t$ for? That part doesn't make sense. – littleO Sep 16 '17 at 12:32
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$T=3\Bbb N$ is a commonly used shorthand for your definition. But yes, your definition works. Just get rid of "$:t$ in there, and write "$T=\{\cdots\}$" directly.
Reading your question a bit more, if you just want to say that $T$ is some set containing only multiples of $3$, but not necessarily all of them, then you shouldn't use $\{\cdots\}$, since those are used for when you want to give an exact description of a specific set. Instead, say that all elements of $T$ are multiples of $3$:$$\forall t\in T\exists n\in \Bbb N(t=3n)$$
Arthur
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But isn't this just another way of writing it and not describing it, although I don't know how it would be done. – nonuser Sep 16 '17 at 08:34
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@johnnobody That's why I called it a shorthand. The actual definition cannot be done much shorter. It is, however, "another way of saying that $T$ is the set of multiples of $3$ in $\Bbb N$", which is what was asked for. – Arthur Sep 16 '17 at 08:52