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## Main Question or Discussion Point

Is the closed interval [a,a] considered a legitimate notation for the set {a}? Would (a,a) denote the empty set?

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Is the closed interval [a,a] considered a legitimate notation for the set {a}? Would (a,a) denote the empty set?

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HallsofIvy

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If I came across reference to an interval like (a,a), I probably would interpret it as the empty set- although I would wonder why they picked a!

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Is a in A? It is if f(x)<0 on [a,a]. And since [a,a] has only one number, it suffices to show that f(a)<0.

A={x : f(x)<0 on (a,x)}

Is a in A? It is if f(x)<0 on (a,a). But this is kind of nonsense. There is nothing in (a,a). You make the call.

So anyway, I just wanted to point this out to show why you might write (a,a) rather than {}.

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