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Q: What numbers have opposites that are the same as their absolute values?

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The absolute value of the answer is the difference between the absolute values of the two numbers and the sign associated with it is the same as that of the number with the greater absolute value.

opposites, additive inverses

An integer that is equal in magnitude to the sum of their absolute values. Its sign is the same as which of the two numbers you are taking the difference from. For example, for the integers 5 and -7. Their absolute values are 5 and 7 so that the sum of the absolute values is 5+7 = 12. Then 5 - (-7) = +12 and -7 - 5 = -12.

The set of whole numbers includes all their additive opposites. So the set is the same as the one you started with.

Assuming that you mean opposites (rather than oppisites), the answer will depend on what kind of opposites: additive opposites or multiplicative opposites.In the first case you have the same set as you started with: whole numbers.In the second, you will have the set that consists of the union ofall whole numbers,all unit fractions between -1 and +1. But, you have a problem with zero: its multiplicative opposite is not defined.

Related questions

Additive opposites MUST have the same absolute values.

The absolute value of the answer is the difference between the absolute values of the two numbers and the sign associated with it is the same as that of the number with the greater absolute value.

opposites, additive inverses

A positive and negative number with the same magnitude (value) will have their absolute values equal.

The absolute value is always non-negative. So, the absolute values of zero and positive integers are the same as the numbers. However, the absolute values of negative integers are their additive inverses or additive opposites (or positive equivalents).Thus, for example, abs(-3) = +3

yes

The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!

The value of the answer is the sum of the absolute values of the numbers and the sign of the answer is the same as that of the two numbers.

Yes.

If "one number" is negative and "another" is positive and the absolute values are the same, then "one number" will be less (because it is negative) than "another" (because it is positive). All negative numbers are less than any positive numbers.

To add a negative number and a positive number: -- Find the difference of their absolute values (their sizes, ignoring their signs). -- Give it the same sign as whichever of the original two numbers had the larger absolute value.

An integer that is equal in magnitude to the sum of their absolute values. Its sign is the same as which of the two numbers you are taking the difference from. For example, for the integers 5 and -7. Their absolute values are 5 and 7 so that the sum of the absolute values is 5+7 = 12. Then 5 - (-7) = +12 and -7 - 5 = -12.

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