# how would write an equation where the answer can greater than, equal to, but not less than zero

how would you modify the equation

a - b = c


so that 'c' could not be less than zero. e.g.

5 - 3 = 2
5 - 4 = 1
5 - 5 = 0
5 - 6 = 0
5 - 60 = 0

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Well if $a-b=c$ and you require that $c\geq 0$ then you require that $a-b\geq 0$ which means you require $a\geq b$. Interpreting your question another way, you can also do

$$|a-b|=c$$

so $c$ will never be negative. Looking at your examples, you can also do

$$\max(a-b,0)=c$$

which coincides exactly with your numerical examples.

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First, you are talking about an inequality which can be stated as thus:

$c\ge0$

Second, the equation $a-b=c$ doesn't state what number system are these numbers from: Natural numbers, Whole Numbers, Integers, Rationals, Reals, Complex, Algebraic, or some other number system? There are more than a few sets of possible numbers so this is something to consider when asking a question.

Third, $5-60=-55$ which does exist in the Integers, Reals, Algebraic, Rationals and a few other number systems. To say that c can't be less than zero but is an integer would be to simply make it a Whole Number in terms of an English statement that is equivalent to the inequality I stated above.

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I think this would refer to the real number system (after a quick check on wikipedia). I thought there might be a way to write a formula so that 'a' and 'b' could equal any real number but 'c' could only equal any real number greater than or equal to '0'. –  JamesHenare Jul 12 '13 at 4:20

The following equation requires $c$ to be non-negative: $a^2 + b^2 = c$ where $a,\,b,\,c \in \mathbb{R}$.

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Is this what you were looking for? –  Alraxite Jul 12 '13 at 4:54