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.

For every element in the field, there is another element such that their sum is equal to , where is the additive identity.

There is an element in the field such that for any element in the field.

We have for any and in the 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.

For every element in the field, there is another element such that their sum is equal to , where is the additive identity.

There is an element in the field such that for any element in the field.

We have for any and in the field.

A field can be defined in many ways.