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# why does negative*negative=positive?

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1. (Original post by IrrationalRoot)
Ha, that's kinda cool actually.
It certainly helped in exams, when I found myself having mental blocks haha
2. (Original post by p29)
"
If 1*x happens when x is rolled. Then -1*y happens when y is not rolled. So if -1 is not rolled, -1*-1=1 because not rolling -1 is a good thing. "
this part confused me
If a bad thing doesn't happen, that makes it good.
3. (Original post by LDS16)
Here's what I remember from Primary:

friend= + enemy= -

A friend of a friend is a friend- + * + = + (positive x positive = positive)
A friend of an enemy is an enemy- + * - = - (positive x negative = negative)
An enemy of an enemy is a friend- - * - = + (negative x negative = positive)
Yes! I tried this way, but using incorrect binary.
4. (Original post by candyaljamila)
PS: This analogy will be more easily understood if you're familiar with vectors, but that's not necessary.

If we have two terms multiplied, "a" being the first term and "b" the second term.

So imagine that when "a" is positive, it is represented by the "Right" direction and when it's negative it's represented by the "Left" direction.

For term "b", when it's positive it leaves you in the same direction, and if it's negative it takes you to the opposite direction.

If the two terms are negative, that leaves us with an "a" located at the "left" and a "b" flipping it to the opposite direction which would be "Right" or "Positive".
This is the only response in the entire thread that I understand lol
5. (Original post by Another)
This is the only response in the entire thread that I understand lol
I just remember negatives come in pairs

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6. (Original post by IrrationalRoot)
Noooooo! Please do not demote mathematics to the level of (lower in this case) physics. Maths has nothing to do with the laws of physics; the laws of physics use maths, but not a single part of maths depends on the laws of physics. Not a single law of physics is even proven to be true.
I don't mean Newton's laws of physics, I mean the physical universe in general. Maths is meaningless unless it describes reality (that's not to say it is always used to describe reality, pure maths is abstract, but it's still ultimately derived from reality.)
7. (Original post by Copperknickers)
I don't mean Newton's laws of physics, I mean the physical universe in general. Maths is meaningless unless it describes reality (that's not to say it is always used to describe reality, pure maths is abstract, but it's still ultimately derived from reality.)
That's a pretty narrow-minded view of maths. I'm happy at the suggestion that maths and understanding the physical world have common roots and common goals still. But maths can describe things which are physically impossible, but still of interest to study (e.g. Banach-Tarski paradox, geometry in dimensions greater than the world we live in) and there are plenty of uses of maths (e.g. RSA cryptography behind internet security) that have nothing particular to do with the physical universe.
8. (Original post by Copperknickers)
I don't mean Newton's laws of physics, I mean the physical universe in general. Maths is meaningless unless it describes reality (that's not to say it is always used to describe reality, pure maths is abstract, but it's still ultimately derived from reality.)
What kind of crazy idea is that? The intellectual exercise that is mathematics is meaningful in its own right.

And how is maths derived from reality? Start with the basics, say the axioms of a number system. How are they "derived from reality"?
9. (Original post by DJMayes)
Let's stop with the rest of this nonsense. No complex numbers, no vectors, no calls to analogous intuitions in other subjects or explanations using debts.

This is a simple and necessary consequence of the rules (axioms) we take for granted in arithmetic:

Put these two together:

Expand the brackets:

Add 1 to both sides (Written as 1 times 1, for reasons you'll soon see):

Factorise the first two terms

A.K.A:

If I hear one more person suggest that this is an axiom or a rule that mathematicians decided then there will be a rampage.

And yes, this is the same thing as @notnek was suggesting, just written out in painstaking detail. Yes you can replace some terms with and if you want to make it more general but there's no point doing that if you're trying to explain this in the first place and it follows incredibly easily from this anyway.
Respect the latex usage, too!
10. (Original post by notnek)
This is an approach I've used in the past when introducing this topic.

Interestingly, the only child who ever asked, "why should the pattern continue" turned out to be one of my best ever students
Indeed. Children who ask questions and particular those that aren't obvious, are usually more apt at this kind of thing (I avoid using the word intelligent, because there are many forms of intelligence).
11. (Original post by Copperknickers)
I don't mean Newton's laws of physics, I mean the physical universe in general. Maths is meaningless unless it describes reality (that's not to say it is always used to describe reality, pure maths is abstract, but it's still ultimately derived from reality.)
I know a good many professors whose work is meaningless by this description. Some would disagree, some would gleefully agree in a very Hardy-esque fashion, but I think that's besides the point I want to really make. The point I want to make is that huge swaths of mathematics have little concern with reality.

I'm happy to expand into specifics but as general topics you have large amounts of algebra, number theory, and in general the various topics broadly concerned only with exploring abstract mathematical structures.
12. (Original post by inhuman)
What kind of crazy idea is that? The intellectual exercise that is mathematics is meaningful in its own right.

And how is maths derived from reality? Start with the basics, say the axioms of a number system. How are they "derived from reality"?
You misunderstood my meaning. What I am saying is that maths is comparable to a language, in that its basic principles are drawn from real observations of things within the physical universe (which does NOT mean physical objects), by which I mean it is empirical. Obviously you can take maths out of the real world and do anything you like with it in the hypothetical world, just like you can with a language. But the point is, if languages are based on observable phenomena, and if maths is based on empirical phenomena, then when they both describe the same thing, they must use the same logic in order to describe them correctly.

Or in simple terms, it is possible to describe mathematical concepts in English without making recourse to allegory: when one says 'X is equal to Y' one is both stating a mathematical concept and also speaking idiomatic English.
13. (Original post by Copperknickers)
You misunderstood my meaning. What I am saying is that maths is comparable to a language, in that its basic principles are drawn from real observations of things within the physical universe (which does NOT mean physical objects), by which I mean it is empirical. Obviously you can take maths out of the real world and do anything you like with it in the hypothetical world, just like you can with a language. But the point is, if languages are based on observable phenomena, and if maths is based on empirical phenomena, then when they both describe the same thing, they must use the same logic in order to describe them correctly.

Or in simple terms, it is possible to describe mathematical concepts in English without making recourse to allegory: when one says 'X is equal to Y' one is both stating a mathematical concept and also speaking idiomatic English.
Again, how are the axioms of number systems drawn from real observations?
14. (Original post by inhuman)
Again, how are the axioms of number systems drawn from real observations?
What else do you think they are drawn from? Do you think they were just made up out of thin air?
15. (Original post by Copperknickers)
What else do you think they are drawn from? Do you think they were just made up out of thin air?
I would not call brain matter thin air.

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