Defining sets

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jwpaine

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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.

{X∈Z∣x≤−10 or x≥5}∪{x∈Z−∣x = 2y  for some  y∈Z}\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: {(−infinity,...,−10) ,(5, ... infinity)}\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\}

Thank you!
 
jwpaine said:
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.

{X∈Z∣x≤−10 or x≥5}∪{x∈Z−∣x = 2y  for some  y∈Z}\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: {(−infinity,...,−10) ,(5, ... infinity)}\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\}
Click to expand...

{−∞⋯ ,−11, −10, −8, −6, −4, −2}∪{5, 6,⋯∞}\displaystyle \{-\infty\cdots,-11,~-10,~-8,~-6,~-4,~-2\}\cup\{5,~6,\cdots\infty\}

Please note how a listing appears.
 
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jwpaine said:
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.

{X∈Z∣x≤−10 or x≥5}∪{x∈Z−∣x = 2y  for some  y∈Z}\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: {(−infinity,...,−10) ,(5, ... infinity)}\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\}

Thank you!
Click to expand...
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.
 
jwpaine said:
would it be correct to say that the above written as a single set: {(−infinity,...,−10) ,(5, ... infinity)}\displaystyle \{ (-infinity,...,-10)\:, (5,\:...\: infinity)\}
Click to expand...

jwpaine,

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


{⋯ ,−11, −10, −8, −6, −4, −2}∪{5, 6,⋯ }\displaystyle \{\cdots,-11,~-10,~-8,~-6,~-4,~-2\}\cup\{5,~6,\cdots\}
 
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