(-1) times (-1) does not equal 1?


Why a negative times a negative should be a positive? (1) Is the enemy of my enemy my friend? Take a look at the following string of equations:

–1 × 3 = –3

–1 × 2 = –2

–1 × 1 = –1

–1 × 0 = 0

–1 × –1 = ?

Now look at the numbers on the far right and notice their orderly progression:

–3, –2, –1, 0, ?

At each step, we’re adding 1 to the number before it. So wouldn’t you agree the next number should logically be 1?

That’s one argument for why (–1) × (–1) = 1. The appeal of this definition is that it preserves the rules of ordinary arithmetic; what works for positive numbers also works for negative numbers.

But if you’re a hard-boiled pragmatist, you may be wondering if these abstractions have any parallels in the real world. Admittedly, life sometimes seems to play by different rules. In conventional morality, two wrongs don’t make a right. Likewise, double negatives don’t always amount to positives; they can make negatives more intense, as in “I can’t get no satisfaction.” (Actually, languages can be very tricky in this respect. The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive, but none in which a double positive makes a negative — to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah”)

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Logic can be illogical.

We just accept what others say and move one…

Two illogical steps make up a logical one. Right? Right?

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