Logical Equivalence
Logical equivalence is an important concept in set-builder notation:
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This means that two sets are equal if and only if their "membership requirements" are logically equivalent.
For example, because, for any real number x, x2 = 1 if and only if |x| = 1; and, therefore, both constructions produce the same set {-1,1}.
Read more about this topic: Set-builder Notation
Famous quotes containing the word logical:
“The logical English train a scholar as they train an engineer. Oxford is Greek factory, as Wilton mills weave carpet, and Sheffield grinds steel. They know the use of a tutor, as they know the use of a horse; and they draw the greatest amount of benefit from both. The reading men are kept by hard walking, hard riding, and measured eating and drinking, at the top of their condition, and two days before the examination, do not work but lounge, ride, or run, to be fresh on the college doomsday.”
—Ralph Waldo Emerson (1803–1882)