The development of number systems

Intro to Number Systems

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• Integers can be represented in the following way
• We can use it for counting and numbering etc!!
• ℤ means {..., −3, −2, −1, 0, 1, 2, 3, ...}.ℤ+ or ℤ> means {1, 2, 3, ...} .
• ℤ* or ℤ≥ means {0, 1, 2, 3, ...} .
• ℤ+ = Represent Positive Integers
• ℤ≥ = Represent non-negative integers excluding Zero
• ℤ = Represents both positive and negative integers including Zero
• Caption: Example representation of Integers

Communicative Property( + and x) only

• These are some properties used with Positive Integers
• 1.Communicative property
• -the variables are interchangeable (think of commuters changing seats in a bus)
• - i.e m + n = n + m (they are interchangeable and the result is the same.
• -i.e (m)(n) = (n)(m) (the only difference here is we are multiplying )
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Associativity property(+ and x)

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• Here the variables can be associated within the parenthesis
• Think of the saying Guilty by Association :-0
• i.e on left and see below also
• i.e m+(n+k) = (m+n)+k
• i.e m(nk) = (mn)k

Distributivity property(+ and x)

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• Here the variable can be multiplied with the other variables with in the parenthesis
• It could be like a an Elephant distributing tickets on a bus :-0
• i.e m+(n+k) = mn + mk
• i.e (n+k)m =m(n+k)
• Caption: Example

Multiplicative and Additive Identity

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• On the Left...........
• <-
• <-
• then to the center.....->
• i.e m.1 = m
• i.e m+0=m
• Self Explained.....
• "It is like an christmas elf on a bus counting candy till he adds the one
• that is zero, then tries to multiply it by one afterwards both the results stay the same..:":-0
• Caption: Example

Decimal example see example 2

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• Caption: Yip thats it

Square roots

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• Caption: Review page 15-16

Additive Inverse

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• Caption: Book Example

Absolute Value

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• Caption: Example

Factoral N

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• i.e
• n!=n(n-1)(n-1)...(4)(3)(1)
• 6! =5-4-3-2-1-0
• Caption: Factoral example

Know the number laws and review exercises

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• Caption: Know this
• Caption: and this