Defining sets

[jwpaine]

Hello! I'm hoping this is the correct sub-forum for set related questions? This is a question from my discrete structures course:

Write the following as a single set using the set-roster notation. You may use elipses (...) if necessary.

\(\displaystyle \{ X \in Z \mid x \leq -10 \: or \: x \geq 5 \} \cup \{ x \in Z^- \mid x \: = \: 2y \:\: for \: some \:\: y \in Z \}\)

Since 'union' includes elements from both sets, would it be correct to say that the above written as a single set: \(\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\} \)

Thank you!

 

[pka]

Hello! I'm hoping this is the correct sub-forum for set related questions? This is a question from my discrete structures course:

Write the following as a single set using the set-roster notation. You may use elipses (...) if necessary.

\(\displaystyle \{ X \in Z \mid x \leq -10 \: or \: x \geq 5 \} \cup \{ x \in Z^- \mid x \: = \: 2y \:\: for \: some \:\: y \in Z \}\)

Since 'union' includes elements from both sets, would it be correct to say that the above written as a single set: \(\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\} \)

\(\displaystyle \{-\infty\cdots,-11,~-10,~-8,~-6,~-4,~-2\}\cup\{5,~6,\cdots\infty\} \)

Please note how a listing appears.

 

[Ishuda]

Hello! I'm hoping this is the correct sub-forum for set related questions? This is a question from my discrete structures course:

Write the following as a single set using the set-roster notation. You may use elipses (...) if necessary.

\(\displaystyle \{ X \in Z \mid x \leq -10 \: or \: x \geq 5 \} \cup \{ x \in Z^- \mid x \: = \: 2y \:\: for \: some \:\: y \in Z \}\)

Since 'union' includes elements from both sets, would it be correct to say that the above written as a single set: \(\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\} \)

Thank you!

Since it is to be written as a single set, I might get carried away and write it as [adding the additional elements added by pka]
{...,-14, -13, -12, -11, -10, -8, -6, -4, -2, , 5, 6, 7, 8, 9, ...}
although just three numbers on each end should be o.k. also.

 

[lookagain]

would it be correct to say that the above written as a single set: \(\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\} \)

jwpaine,

you wouldn't bother to put an infinity symbol in there, because each ellipsis means "it goes on forever."


\(\displaystyle \{\cdots,-11,~-10,~-8,~-6,~-4,~-2\}\cup\{5,~6,\cdots\} \)

 

[jwpaine]

Understood. Thank you all!