Transcript Sets of numbers

Sets of numbers
Sets of numbers
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Natural (Counting) Numbers {1, 2, 3, 4, …}
Whole Numbers {0, 1, 2, 3, …}
Integers {…, -2, -1, 0, 1, 2, …}
Rational Numbers: A number that can be
expressed in the form a/b, where a and b are
integers, and b ≠ 0, is a rational number.
• Irrational Numbers: A non-repeating (neverending) decimal.
• Real Numbers: Rational and Irrational numbers
combined, form the set of real numbers
Closure
• Def: A set is closed under an
operation when every pair of
elements from the set, under the
given operation, yields an element
from that set.
Closure
• The set of integers • The set of integers
is closed under the
in not closed under
operation addition.
the operation
division
Disjoint sets
• Def: Two sets are disjoint sets if
their intersection is the empty set.
That is, if they do not have any
elements in common.
• EX: The set of rational numbers and
the set of irrational numbers are
disjoint.