JackieCortes
JackieCortes JackieCortes
  • 02-02-2017
  • Mathematics
contestada

Which operations is the following set closed under: {... , -3, -1, 1, 3, ...}?

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LammettHash
LammettHash LammettHash
  • 02-02-2017
Not addition, since [tex]-1+1=0[/tex] and 0 doesn't belong to the set.

Not subtraction, since [tex]1-1=0[/tex].

It is closed under multiplication. The set appears to contain all non-zero multiples of 3.

Not division, since dividing some of the numbers results in rationals which do not belong to the set.

What other operations are you supposed to consider?
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AL2006
AL2006 AL2006
  • 02-02-2017

I'd say it's closed for multiplication and division.
Any member of the set, when multiplied or divided by
any other one, produces another member of the set.
Answer Link

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