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?
Answer Link
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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