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In Algebra we care about different sets of numbers and which numbers are part of different sets. Natural Numbers. Natural Numbers • 1, 2, 3, 4, 5, …. Natural Numbers • 1, 2, 3, 4, 5, … • Numbers we count with.
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In Algebra we care about different sets of numbers and which numbers are part of different sets.
Natural Numbers•1, 2, 3, 4, 5, …• Numbers we count with•Positive whole numbers
Natural Numbers•1, 2, 3, 4, 5, …• Numbers we count with•Positive whole numbers• Symbol = N
Whole Numbers•0, 1, 2, 3, 4, 5, …• Natural numbers & 0•Symbol = W
Integers• … , -3, -2, -1, 0, 1, 2, 3, …•Whole numbers and their opposites
Integers• … , -3, -2, -1, 0, 1, 2, 3, …•Whole numbers and their opposites•Symbol = Z
Rational Numbers•Symbol = Q• Numbers that can be written as the quotient of two integers
Rational Numbers•Symbol = Q• Numbers that can be written as the quotient of two integers• “Normal” fractions
Rational Numbers•For example … ¾ 5/3 -½ 34/7 2.25 -.66666…
Rational Numbers•For example … ¾ 5/3 -½ 34/7 2.25 -.66666… 42 -11
Rational Numbers•Symbol = Q• Numbers that can be written as the quotient of two integers• “Normal” fractions
Irrational Numbers•Symbol = I or Ir• Not rational• Can’t be written as a quotient of integers• “Weird” numbers
Examples of Irrational Numbers•Square roots you can’t simplify
Examples of Irrational Numbers•Higher roots you can’t simplify
Examples of Irrational Numbers•Most trig function values sin(52) tan(107)
Examples of Irrational Numbers•Decimals that don’t end and don’t repeat .27227722277722227777…
Real Numbers•Symbol = R• Rational and irrational numbers together
Real Numbers•Symbol = R• Rational and irrational numbers together• Every number on the number line
Real Numbers•Symbol = R• Rational and irrational numbers together• Every number on the number line• Every number you know
A field is just any set that has the same properties as the real numbers.• The properties of numbersare essentially the postulates of algebra.
3 + 5 = 5 + 32(-9) = -9 2Order doesn’t matter when you add of multiply.
-17 + (17 + 39) = (-17 + 17) + 39(7 4) 9 = 7(4 9)You can group together what you want to when you add of multiply.
7 + 0 = 4 0 + 2 = 25 1 = 5 1(-4) = -4When you add 0 or multiply by 1, you get back what you started with.