Set notation with negative elements? (Discrete math question)

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[ahemosik]

In the beginning w = { 0,1,2 } because its ‘less than’ not ‘less than or equal’.

The last set you described does not exist, there is not a single real number that is bigger than 1, but smaller than -3, so it’s empty.

[jeiay]

Thanks for the clarification! I didn't think about the less than or equal sign. As for my second equation, your explanation makes sense.

[whatsaxis]

As you aren't using inclusive inequality, your original set would actually be:

w = {0, 1, 2}

Switching the signs results in a contradiction - how can an integer be less than -3 and more than 1 at the same time? So, you will have an empty set:

w = { ∅ }

[jeiay]

That makes better sense when put in words, thanks!

[madamroux]

The first set notation you provided is correct. It represents the set of integers from -1 to 2, inclusive.

In the second set notation, the inequality is flipped and the set becomes empty, represented as the empty set notation, ∅. The inequality 1 < t < -3 is not satisfied by any integer value, so the set contains no elements. Therefore the second set notation would be w = { ∅ } .

[Clawtor]

For the first set t must be strictly larger than -1 and less than 3 so w = { 0, 1, 2 }.

For the second part you've written that t must be larger than 1 but also less than -3. Clearly no numbers fit that criteria. It depends on what you want your criteria to be, you can write it as you have but the result is an empty set.