N NATURAL NUMBERS positive, integer negative, integer Z INTEGERS not integer

but rational numbers Q RATIONAL NUMBERS e.g. 0.5, 1/3 numbers which can be obtained by dividing two integers Q IRRATIONAL NUMBERS real numbers which can't be obtained by dividing two integers eg. √2, π, e + R REAL NUMBERS a real number is a value that represents a quantity along a continuous line (the NUMBER LINE) C COMPLEX NUMBERS a complex number is a number which can be put in a form a+bi,

where a and b are real numbers

and i=√-1 in the REAL SET of numbers however there are many equations which contain expressions like this, and can't be solved among the reals a negative number can't be under a square root (WHOLE NUMBERS) 0 8 - 8 COMPLEX NUMBERS extend the idea of the one-dimensional number line to the two-dimensional complex plane. REAL IMAGINARY (0;0) a b a+bi complex numbers have a real part (a) and an imaginary part (bi).

so if a=0 the number is purely imaginary,

if b=0 the number is real THESE SETS ARE THE MOST USED ONES IN MATHEMATICS. COMPLEX NUMBERS in order to solve them we need to use (imaginary unit) (and zero) 0 4 3 2 1 -4 -3 -2 -1 -5 0 4 3 2 1 6 5 -4 -3 -2 -1 -5 .. . . . .... . . .. . . .. .... . . . ... ... . . 0 -1 0.5 1 .. . . . .... . . .. . . .. .... . . . ... ... . . .. . . . .... . . .. . . .. .... . . . ... ... . . (~2.718) e π (~3.14) (~1.414) √2 ... . . . . .. . . . . ... . ... ..... . . . . ... . . . .. . . ... ... .. .. . ... . . . . .. . . . . ... . ... ..... . . . . ... . . . .. . . ... ... .. .. . ... . . . . .. . . . . ... . ... ..... . . . . ... . . . .. . . ... ... .. .. . but with only them, how could we solve

3+x=2? we need negative numbers! so we have all the integers, but there are things again which can't be solved, for example on our number line, there are holes now. we need to fill them with new numbers. now please solve x +1=0. 2 2x=7 together they make up the set of... you can't?

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# NUMBER SYSTEMS

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