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anonymous
 4 years ago
What does it mean if a set is "closed with respect to addition?" What about multiplication?
anonymous
 4 years ago
What does it mean if a set is "closed with respect to addition?" What about multiplication?

This Question is Closed

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1It means that whenever you add any two members of the set your answer is also a member os the set.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'll give you sets and will you tell me if they are? {1,2}I think no because there is no 3 {1,2,3} think yes because 1+2=3 {1,2,3,4}would it be because 1+2 = 3, or would it not be because 1+4 = 5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0If it's the same way for multiplication, does that mean any set with a one and something else in it is closed to multiplication?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1the set of all positive numbers is closed under addition: whenever you add positive numbers you get another positive number as an answer {1,2} is not closed under addition because 1+2=3 and 3 is not a member of the set {1,2}. it is closed under multiplication though, because 1*2=2 which is an element of the set

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1(the set of positive real numbers is also closed under multiplication too)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so it just has to have at least one number in it that is the sum or product of two other numbers in it?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1no, {1,2,3} is closed under neither addition nor multiplication, because 3+1=4 (not a member) and 2*3=6 (not a member) so as long as there is any way to produce a member outside the set, that set is not closed under that operation.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1...no matter that 1+2=3, there exists a way to create an element outside the set, so it is not closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0are you sure? it seems like I heard differently. But I'm unsure so I'll go with you.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1My understanding is as I said it, and quoting mertsj: "It means that whenever you add any two members of the set your answer is also a member os the set." seems like that's the same thing here's something from online: http://mathforum.org/library/drmath/view/52452.html
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