Page 40 - 'Blast_Into_Math

Blast into Math! ets of nummers: mathematical plaagrounds

According to these rules, the integers are closed under addition, subtraction, and multiplication. The
integers Z are a bigger playground than N because they contain additive inverses, which is like having
an addition swingset. Starting at the additive identity 0, we can swing over to an element of N like 3,
and then we can get a push over to its additive inverse −3, add them together and end up back where
we started at 0. Is there also a multiplication swingset in the playground Z? If we have an integer x ,
then is there a number, y so that

xy =1?

The number y would be the multiplicative inverse for x , and we would write

1
y = .
x

If x =2, we can solve the equation for y ,

2y =1,

so

1
y = .
2

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