In junior high school algebra we are taught that the product of two negative numbers is a positive number. This is not all that intuitive and there is a maxim which states that "Minus times minus is plus. The reason for this we need not discuss." Can anyone produce a proof that -1 * -1 = 1
Philosophically........ if........ the "Evil Satan" is actually a lot like Stanley Milgram Ph. D...... and is actually ACTING EVIL..... rather than truly being evil......... then "Satan" ........ could actually be one of the greatest servants of YHWH / The G-d of Abraham / HaShem in the Universe / Multiverse??????? https://www.simplypsychology.org/milgram.html I get Philosophy, Theoretical Physics and Mathematics mixed up a lot?! Sorry?! www.CarbonBias.blogspot.ca/
The real question is in application within the real world, and not what can and cannot exist in the theoretical world of math. Outside of human constructs, where exactly do negative numbers even exist?
Everything in math is simply definitional and as such axiomatic. You try to reduce your axioms to the least possible number by introducing logic and theorems. A theorem is a theory that has been proved deductively.
Math and time do not really exist. They are simply products of the human mind. If humans ceased to exist then math and time would also cease to exist.
It makes sense in electricity and in computerized calculations. The only thing that computers don't like is dividing by zero.
All math begins with counting. It was the prehistoric men who were counting elk (European red deer) on a hunting trip which gave rise to the first mathematics. Then the ancient Babylonians, Egyptians, and Greeks all at about the same time came up with geometry for building fortress walls, temples, and cities. The Arabs invented Algebra (or stole it from the Hindu's) to solve simultaneous linear equations. "Fatima has 2 baskets of figs. A basket holds 50 figs. How many figs does Fatima have?" x = 2y y = 50z x = 2(50) = 100 figs.
Negative numbers is best explained and applied to debt in accounting. "A newly incorporated business has $300 in cash. This cash was obtained by the two owners contributing $100 each and the bank loaning $100 more to them." Debits = $300 in the cash account. Credits = $100 to owner A, $100 to owner B, and $100 owed to the Bank. $300 debits = $100 + $100 + $100 credits. $300 debits = $300 credits. Debits + Credits = -0-. Ergo the credits are negative numbers and the debits are positive numbers.
-1 * -1 = 1 is a theorem. Can you find the proof? (Hint: start with the axiomatic equation 0 * 0 = 0)
I'm not so sure. I AM sure I'm not a physicist! So, check this out: Einstein and others gave us the idea that this universe is space-time. Time is just one of the dimensions. Thus, there is no "before" the big bang, as time came as a dimension of this universe, not something that extends to some other universe. The notion that time is independent of humans or events came with Newton, as I remember. Before that, time was a matter of sequencing events - it wasn't as if time was an independent thing. After Newton, relativity gave a more solid idea of time. If humans go away, that won't change the fundamental structure of the universe. So, time will be what it is now, I think, until something truly stupendous happens or the universe finally evaporates to nothingness as is currently projected.
No. It is a theorem. I can prove it from Peano's axioms and the distributive law (which is a theorem of the same axioms.) 0 * 0 = 0 (1+(-1))(1+(-1)) = 0 as -1 is defined as the additive inverse of 1 0=(1+(-1))(1+(-1)) = 1+2(-1) + (-1)(-1) (distributive law twice) so ... 0 = 1 - 2 + (-1)(-1) = -1 + (-1)(-1) (as 1-2 = -1) thus ... 0 = -1+(-1)(-1) adding 1 to both sides yields... 1 = (-1)(-1) QED
That's a human construct. More accurately, a temperature gauge would start at absolute zero, and go up from there. (not as practical, though)
Its inherent in number theory. If (-1)(-1) does not equal +1, then the distributive property does not hold for negative numbers and the entire mathematical system breaks down. Or z = xy + (-x)(y) + (-x)(-y) = xy + (-x)(y-y) = xy - x(y-y) = xy and z = xy + (-x)(y) + (-x)(-y) = x(y-y) + (-x)(-y) = (-x)(-y) z has to equal z so xy = (-x)(-y) so a neg times a neg is a pos
Negative numbers were invented by the Chinese. They are simply an invention. They are whatever you want them to be. You can define them as anything.
If you define them as something other than what they are you can't do mathematics and are living in the dark ages.
Math does not really exist. It is merely an invention of the human mind. Like ethics. Math is whatever you invent and define it to be.
If we take x^x and set x to 0.0001, it approaches 0.999079 That isn't a proof though. I've done some analysis on this, and for a graph of y=0^x if 0^0 does equal 1 then the slope at the seeming discontinuity must be infinitely steep. It's not clear whether this function is discontinuous, in an abstract theoretical point of view, an interesting mathematical problem. That is to say, there must be some point where 0^x equals a range of values between 1 and 0 but the interval is so infinitely small there are no actual real numerical values that would satisfy the criteria.
Here's a proof that 0^0 does not equal 0. As you know y=0^x is essentially a straight line with the equation y=0, with the exception of the point x =0. If it truly was a straight line with the equation y=0 then it should intercept a line with the equation y=x at the point (0,0). y=0^x , y=x using a little bit of substitution y=0^y divide both sides by y 1=0^[y-1] 1^[1/[y-1]]=0 now, if we try to substitute y with 0 at this point 1^[1/[(0)-1]]=0 1^[1/-1]=0 1^[-1]=0 1^[1/1]=0 1^1=0 1=0 so x=y does not intercept y=0^x at (0,0)
