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7.1.  The Number Systems:

7.1.1.     The number system: Be able to perform all + - * / ^ operations with all types:

7.1.2.     Integers

7.1.2.1. Positive integers / whole numbers (counting)          1, 2, 3,…  Know + - * / a^b  = a^b

7.1.2.2. Negative integers (inverse addition)  -1, -2, -3… from  3 + x =0 or x = -3

7.1.2.3. Zero – for a long time this was not a number, It was not apparent that a symbol for nothing was needed

7.1.3.     Rational numbers / fractions = a/b (ratios of integers from inverse division and multiplication)  a * x =1 or x=1/a

7.1.4.     Irrational numbers / non-repeating decimals (from inverse exponentiation) a^b  such as  (2)^1/2,  also p, e, f

7.1.5.     Complex numbers  (also from inverse exponentiation with negative numbers)(-1)^1/2  = i

7.1.5.1. imaginary numbers and complex values = a + ib

7.1.5.2. With infinity, the complex numbers close under all operations.

7.1.6.     Infinity:  Cantor – concept of 1 to 1 matching – multiple levels of infinity

7.1.6.1. Infinity of counting 1,2,3,…  Note same value as even integers

7.1.6.1.1.     Same as the infinity of rational numbers a/b

7.1.6.2. Infinity of real numbers

7.1.6.3. Infinity of functions

7.1.7.     ‘Scientific numbers’:  1.23456E3 = 1.23456*10³ = 1234.56  likewise   4.56E-2 = 0.0456

7.1.8.     ‘Uncertain numbers’ (numerical uncertainty or fuzzy numbers)  1.23 = 1.23???...  Problems:

7.1.9.     ‘Order of magnitude numbers’  2E32 or maybe just 1E32 and calculations. Problems: