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Why is the additive inverse of a positive number always negative?
Wiki User
∙ 10y ago
The short answer is because of the definition. A longer answer is:
Start of with a negative number X whose additive inverse is Y. SUPPOSE Y is not positive.
Then X + Y is
one negative, X,
less another number that is at most 0, Y.
So their sum is less than or equal to X. That is, X + Y is at least as negative as X (and possibly even more negative).
But if Y is the additive inverse of X then, by definition (of additive inverses), X + Y MUST be 0.
That is a contradiction. So somewhere down the line there is an incorrect supposition. The only supposition above is that Y is not positive. So that supposition must be incorrect. Therefore Y is positive.
Wiki User
∙ 11y ago
Wiki User
∙ 10y agoWhen you put them opposite each other on the number line the negatives are opposite to the positives.
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Is the opposite of a negative number always sometimes or never a negative number?
never a negative number * * * * * ... true if, by opposite, you mean the additive inverse. However, the multplicative inverse is also an opposite. And the multiplicative inverse of a negative number is always negative.
Find the sum of the opposite of -18 and its additive inverse?
The additive inverse of -18 is +18.Hence if you want to add them,Remember the additive inverse of a negative number will be its positive.Its simple, just remove the negativity symbol. So -5 additive inverse is +5.And for a positive number just put a negativity symbol in front of it. :D.Hence +10 will become -10.Remember the additive inverses always add up to give zero!!Therefore you can always use this way to find the answer of your question.Let the additive inverse of -18 be X.As the law states, they add up to 0-18 + X = 0X = 0- (-18)X = 0+18X = 18Coming to the next part of your question,the opposite of -18 is simply the additive inverse!!!Therefore its 18!!Hence18+18=36!Hope that helps buddy!!
What is the opposite of the absolute value of 8?
The additive opposite is negative 8 (-8). Absolute values are always positive numbers.
Will the opposite of a number always sometimes or never be greater than the number itself?
Sometimes. Also, when depends on what you mean by "opposite": the additive inverse or the multiplicative inverse.
Why is the sum of two negative integers always negative?
They are always negative due to a negative plus a negative equaling a negative. It's similar to a positive plus a positive equaling a positive.
What the additive inverse of 0?
The number 0 (zero) is the alpha and the omega when it comes to neutrality. It always was, is, and always will be neutral. 0 (zero) is neither positive nor negative. Thus, the additive or negative inverse of 0 (zero) is 0 (zero).
Is the opposite of a negative number always sometimes or never a negative number?
never a negative number * * * * * ... true if, by opposite, you mean the additive inverse. However, the multplicative inverse is also an opposite. And the multiplicative inverse of a negative number is always negative.
Will additive inverse always equal 0?
When a number is added to its additive inverse, the result is always 0.
Are absolute value and additive inverse equal why?
No. This is because absolute values are always positive. For example: |2|=2 absolute value Additive inverse means the opposite sign of that number so 2's additive inverse is -2. But sometimes if the number is -2 then the additive inverse equals the absolute value. therefore the answer is sometimes
Find the sum of the opposite of -18 and its additive inverse?
The additive inverse of -18 is +18.Hence if you want to add them,Remember the additive inverse of a negative number will be its positive.Its simple, just remove the negativity symbol. So -5 additive inverse is +5.And for a positive number just put a negativity symbol in front of it. :D.Hence +10 will become -10.Remember the additive inverses always add up to give zero!!Therefore you can always use this way to find the answer of your question.Let the additive inverse of -18 be X.As the law states, they add up to 0-18 + X = 0X = 0- (-18)X = 0+18X = 18Coming to the next part of your question,the opposite of -18 is simply the additive inverse!!!Therefore its 18!!Hence18+18=36!Hope that helps buddy!!
Can additive variance have a negative value?
No. Variance is always positive and so the sum of variances must also be positive.
How is absoulute value different from positive and negative integers?
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
Is inverse of a function always positive?
No.Some functions have no inverse.
What are the characteristics of absolute value?
They are always non-negative. The absolute values of any number and its additive inverse are the same: that is f(-x) = f(x) for all x.
What is the opposite of the absolute value of 8?
The additive opposite is negative 8 (-8). Absolute values are always positive numbers.
Will the opposite of zero always or never be zero?
The opposite of zero - in the sense of additive inverse - is zero.
Is it true that a number is always greater than its opposite?
No, not at all!I'll assume you mean the additive inverse, although the following examples can be adapted to the multiplicative inverse as well.The additive inverse of 5 is -5, and 5 is indeed greater than -5.However, the additive inverse of -5 is 5, and -5 is SMALLER than 5.
