Precalculus : Real Numbers
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Example Questions
Example Question #1 : Real Numbers
Which of the following is not true about a field. (Note: the real numbers is a field)
A field can be defined in many ways.
For every element in the field, there is another element such that their product is equal to , where is the multiplicative identity, in the case of real numbers.
We have for any and in the field.
There is an element in the field such that for any element in the field.
For every element in the field, there is another element such that their sum is equal to , where is the additive identity.
For every element in the field, there is another element such that their product is equal to , where is the multiplicative identity, in the case of real numbers.
It is not the case that for any element in a field, there is another one such that their product is . Take in the real numbers. Multiply by 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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