This is gorgeous, because, indeed, it amounts to 0. Now, look at the term between the large brackets. Guess what, we can do the same for the two terms above, but with $(-b)$ instead:
Negative plus a positive equals how to#
Remember how to factorise? After factorising, something like $pq + pr$ becomes $p(q+r)$, for example. Now, let us replace the number 0 by variables-just the variables we are using here, to be exact. Or, to be a little more pedantic about notation, we could write it more compactly as So, let’s rewrite the expression as follows: If the reverse is true, the answer is a negative. In fact, for any positive value of x, or if x equals zero, the sign would. If the absolute value of the positive is greater than the absolute value of the negative, the answer is positive. Absolute values are never negative, because absolute value only asks how far. Still a true thing, right? Now, what is also true: anything multiplied by zero equals zero. It depends upon what the positive and negative may be. Now, let us add a term without disturbing the essence of the expression: The following may seem obvious but bear with us. Hence, we write the above equation as if we were actually earning an honest living: So, of course, for their employer’s money’s worth, they will almost never bother to properly write down the ‘$\times$’-sign. They can truly be a productive lot sometimes. Mathematicians are true masters of multiplying almost anything at almost any time and even manage to get paid for it. (I put the negative numbers $-a$ and $-b$ between brackets for better visibility, not because they represent any extra information or some sort of an afterthought in the literalistic sense, which this sentence totally does.)
We also learnt in high school that multiplying a negative number with another negative number equals some positive number. Which is, clearly, in this universe, utterly ridiculous. I mean, just in case it’s not quite clear yet, let’s suppose $(-b) = c$, so, replacing $(-b)$ with $c$, we get You can see now, we have a contradiction. Just to add some clarity, I’m going to slap some brackets around $-b$ on the right hand side:
Let’s first pretend the opposite is true. Okay, so let’s prove that, shall we? Or shall we…? Well, not yet. Now, using just variables instead of numbers, we can write this as In human English language, it should sound something like: ‘One minus minus two equals one plus two equals three’. We all should have learnt in high school that subtracting a negative number is the same as adding the positive version of that number. Requirements: simple algebra from the second year in secondary, high or grammar school. Even though you will know this already, here you will find an algebraic proof, just for your reference. You may have heard or uttered these expressions many times.
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