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What represents fractions?
Q represents the set of all rational numbers, Zrepresents the set of all integers so Q excluding Z, represents all rationals that are not integers.
10 P for Q and Z in S?
10 points for Q and Z in Scrabble.
What is meant by a subgroup generated by an element x belongs to group G?
It is a subset of the Group G which has all the properties of a Group, namely that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. The set of integers, Z, is a Group, with addition as the binary operation. [It is also a Ring, but that is not important here]. The set of all multiples of 7 is a subgroup of Z. Denote the subgroup by Z7. It is a Group because: Closure: If x and y are in Z7, then x = 7*p for some p in Z and y = 7*q for some q in Z. Then x + y = 7*p + 7*q = 7*(p+q) where p+q is in Z because Z is a Group. Therefore 7*(p+q) is in Z7. Associativity: If x (= 7p), y (= 7q) and z (= 7r) are in 7Z, then (x + y) + z = (7p + 7q) + 7r since these are in Z an Z is associative, = 7p + (7q + 7r) = x + (y + z). Identity: The additive identity is 0, since 0 + x = 0 + 7p = 7p since 0 is the additive identity in Z. Invertibility: If x = 7a is in Z7 then 7*(-a) is also in 7Z. If 7*(-a) is denoted by -x, then x + (-x) = 7a + 7*(-a) = 0 and so -x is the additive inverse of x. But there are elements of Z, for example, 2 which are not in Z7 so Z7 it is a proper subset of Z.
How can you represent how the sets of whole numbers integers and rational numbers are related to each other?
Whole numbers and integers are identical sets. Both are proper subsets of rational numbers.If Z is the set of all integers, and Z+ the set of all positive integers then Q, the set of all rational numbers, is equivalent to the Cartesian product of Z and Z+.
What is the mathematical equation for Z is 6 less than two fifths the value of Q?
z = 2q/5 - 6
