The development of number systems

Slide 1

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Intro to Number Systems

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 Integersℤ≥ = Represent non-negative integers excluding Zeroℤ = Represents both positive and negative integers including Zero

Caption: : Example representation of Integers

Slide 2

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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Slide 3

Associativity property(+ and x)

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

Slide 4

Distributivity property(+ and x)

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

Caption: : Example

Slide 5

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Multiplicative and Additive Identity

On the Left...........<-<-then to the center.....->i.e m.1 = m i.e m+0=mSelf 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