Does any one know what this quantifier means in English and its truth value?
∀x ∈ Z (X^2 ∈ Z)
2007-09-13 04:15:11 · 3 answers · asked by Carlos 2 in Science & Mathematics ➔ Mathematics
For all "x" in the set of integers, x^2 is an integer.
or
The square of every integer is an integer.
REgards,
Chas.
2007-09-13 04:21:40 · answer #1 · answered by Chas. 3 · 0⤊ 0⤋
The quantifier â means "for all". So, this statement reads as
For every x in Z, x^2 is in Z.
2007-09-13 11:37:11 · answer #2 · answered by Steiner 7 · 0⤊ 0⤋
This means that if you have a random x that belongs to Z, then that same x elevate to the 2 exponent will belong to Z as well.
Z = all numbers negative and positive (not including fractions, sqrt...)
Z={ ..., -3,-2,-1,0,1,2,3...}
Example:
-3 belongs to Z
(-3)^2 = 9 and 9 also belong to Z
2007-09-13 11:19:34 · answer #3 · answered by Carla 4 · 0⤊ 0⤋