Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. the set of natural numbers.

Chardonnay Felix 2021-01-16 Answered
Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. the set of natural numbers.
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tabuordg
Answered 2021-01-17 Author has 99 answers

The set of natural numbers is {1,2,3,4,}.
The additive identity of a number, aa, is always 0 since a+0=0+a=a. Since 0 is not included in the set of the natural numbers, then the set does not have an additive identity.
The additive inverse of a number aa is −a since a+(a)=a+a=0. The set of natural numbers does not include any negative numbers so for all natural numbers a, the additive inverse of −a would not be a natural number. The set then does not have an additive inverse.
The multiplicative identity of a number aa is always 1 since a1=1a=a. Since 1 is included in the set of the natural numbers, then the set does have a multiplicative identity does have a multiplicative identity.
The multiplicative inverse of a number aa is always 1a since a1a=1. If aa is a natural number not equal to 1, then 1a is not a natural number. For example, a=2 would have a multiplicative inverse of 1a=12 which is not a natural number. The set of natural numbers then does not have a multiplicative inverse. ​

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