Basic set theory / mathematical notation

[jaejoon89]

I'm supposed to write the following intervals as sets in descriptive form:

a. (t, infinity), t a fixed real number

b. (0, 1/n), n a fixed natural number

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I think it is:
a. (t, infinity) = {x: t < x < infinity}
b. (0,1/n) = {x: 0 < x < 1/n}

Is this correct?
Also, how do you indicate that t is a fixed real number and n a fixed natural number?

 

[snipez90]

This seems fine. The only comment I will make is that I don't think you need the infinity in the "descriptive form". The extended real number system is defined so that {x: t < x} would suffice, iirc.

 

[n!kofeyn]

a. (t, infinity) = {x: t < x < infinity}
b. (0,1/n) = {x: 0 < x < 1/n}

Is this correct?
Also, how do you indicate that t is a fixed real number and n a fixed natural number?

I agree with snipez90's comment. Also, it would be good to be explicit about what x, t, and n are. You would notate this as $x\in\mathbb{R}$. To say that t is a fixed real number, just say $t\in\mathbb{R}$, and to say that n is a fixed natural number, just say $n\in\mathbb{N}$.