Precalculus : Real Numbers

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 :Define A Field

Which of the following is not true about a field. (Note: the real numbersis a field)

Possible Answers:

For every elementin the field, there is another elementsuch that their sumis equal to, whereis the additive identity.

There is an elementin the field such thatfor any elementin the field.

For every elementin the field, there is another elementsuch that their productis equal to, whereis the multiplicative identity,in the case of real numbers.

We havefor anyandin the field.

A field can be defined in many ways.

Correct answer:

For every elementin the field, there is another elementsuch that their productis equal to, whereis the multiplicative identity,in the case of real numbers.

Explanation:

我t is not the case that for any elementin a field, there is another onesuch that their product is. Takein the real numbers. Multiplyby any number and you get, so you will never get. This is true for any field that has more than 1 element.

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