2 edits
Originally posted by RolfeyWell since maths in general is man-made then the rules for negative
so, -2 multiplied by -2 equals positive 4. i understand how this works (but can't explain it well so look it up if you disbelieve me). what i want to know is as this rule was man made does this make our maths wrong?!
discuss!
numbers would be manmade also but they are there because it has
been provent to work. I read a book once, actually worked with the
author, a guy named Malcom Lines, wrote this book called
'a number for your thought' and its a great little book. It sure
blew Isaac Asimov away when he read it and that started a life long
correspondence between the two. One of the points of the book is
you can use negative numbers even in making a number system.
That is, right now, if you say the number 124, you mean one of the
class of 100's, added to 2 of the class of 10's and 4 of the class of
units, so 100 plus 20 plus 4. That is one of 10 ^2, 2 of 10^ 1 and
4 of 10^0. Notice that is 10^2, the ^2 part is a positive 2.
Malcom says you can base a number system on negative 2 or -3 or
-4 or whatever. Any positive or negative number can be denoted with
a negative exponent system. Think about THAT one for a while!
Its a great little book, a number for your thoughts, if you can find it.
Try doing the math as you said, -2 times -2 = plus 4.
But try fooling around with your premise, which is why can't
-2 times -2 = -4.
That would be a zero line centric math, heck it might even work but
I don't think so. That is to say everything in math would center about
the zero point, with numbers going positively from zero and ones
going negatively from zero. The actual number line is set up that way
of course. Why is there a differance between (-2) plus (-2)
and (-2) MINUS (-2)?
I think you have to think of these kind of number problems as
just steps on a ladder, like if you are at -5 on some grid and
you go up 6, that is to say add +6, you end up at the plus one point.
That makes the zero point just a referance point and not some
all important black hole of math that everything runs around.
Get the differance?
here is a link to positive and negative numbers explained:
http://www.mathleague.com/help/posandneg/posandneg.htm
Originally posted by RolfeyThe reals are a field. 1 is in the field, so it has an additive inverse, -1, such that -1+1=0. -1 has a multiplicative inverse, say (1/-1), such that -1*(1/-1)=1. Thus 0 = -1*(1/-1)-1. Multiplication is distributive over addition in fields, so 0= -1*((1/-1)+1). Fields are integral domains, so there can be no nonzero divisors of 0, and -1 is not 0, so (1/-1)+1=0. Thus 1/-1 is the additive inverse of 1, and since the field is a group under addition, additive inverses are unique. But -1 is the additive inverse of 1. Thus -1 = (1/-1). Thus (-1)*(-1) = 1.
so, -2 multiplied by -2 equals positive 4. i understand how this works (but can't explain it well so look it up if you disbelieve me). what i want to know is as this rule was man made does this make our maths wrong?!
discuss!
Now (-1)*2+2 = 2(-1+1) = 0, so (-1)*2 is the additive inverse of 2, ie -2. Thus (-2)*(-2) = (-1)*(-1)*2*2 (by associativity of multiplication), and by the previous result, this is equal to 2*2, which you've called 4.
I haven't been totally anal-retentive about saying where I've used which axioms, but all of these follow from the axioms defining a field. (In fact, we needn't even go that far, since no use is made of multiplicative inverses of non-unit elements; it suffices to use the fact that the structure in question is an integral domain. However, I think you were really getting at the fact that multiplying two negative REALS give a positive one, in which case a better starting question would have been to use pi and -pi or something.)
The point is that all of that follows from some well-defined set of axioms--in principle, anything in mathematics is an immediate consequence of some set of essentially arbitrary axioms together with some rules for deductive reasoning. Most mathematical axioms, in practice, reflect direct experience. However, that is a matter of choice.
This does not mean, however, that mathematics is 'man-made' in the sense you describe. What we really mean when we assert a mathematical truth A (which is relative to axioms) is the axiom-independent statement 'the negation of A, together with these axioms, entails a contradiction'. In this way, truths of (axiomatic) mathematics correspond to logical truths, so the question of man-madeness is removed to the strictly logical realm.
The rules of logic can be axiomatised as well. However, as I see it, this is essentially different from axiomatising mathematics, because I can easily imagine an axiom-system governing some object which contradicts another axiom-system, and this causes no problems. However, changing a logical axiom removes our whole mode of reasoning and communication; I think such a change is literally unimaginable.
If you think mathematics is man-made (that's a bit chauvanistic; I know plenty of very good female mathematicians!), consider what would happen if you invented some new mathematical object with certain properties, proved a variety of theorems about it, and then were struck by a bus and killed on the way to explain it to your colleagues. Also suppose that the bus rendered all of your papers illegible and that you had not communicated these ideas to anybody beforehand. Do your theorems still exist, or has mathematics reverted to the state it was in before your discovery?
Originally posted by RolfeyI always find it easist to explain from the pattern
so, -2 multiplied by -2 equals positive 4. i understand how this works (but can't explain it well so look it up if you disbelieve me). what i want to know is as this rule was man made does this make our maths wrong?!
discuss!
2x4=8
2x3=6
2x2=4
2x1=2
2x0=0
.......... Therefore - continue the pattern you get
2x-1 = -2
2x-2 = -4. Spin this round and you get
-2 x 2 = -4 (above but swapped)
-2 x 1 = -2
-2 x 0 = 0
-2 x -1 = 2
-2 x -2 =4
Hope that helps
1 edit
Originally posted by RolfeyEverything created by humanity (man is a gender byast word) is flawed as is our nature 😉
so, -2 multiplied by -2 equals positive 4. i understand how this works (but can't explain it well so look it up if you disbelieve me). what i want to know is as this rule was man made does this make our maths wrong?!
discuss!
Originally posted by sasquatch672Yeah, but people tend to say 'math' with a patronising air that evokes a lot of boring algorithms for doing boring things you meet in school, while 'maths' connotes a beautiful branch of philosophy.
Okay - here's the real question. Why do you euros call mathematics "maths"? It's infuriating. The short name - "math" - is a collective plural that encompasses the field of study. Adding the "s" is redundant. Why do you all do it?
1 edit
Originally posted by sasquatch672being english i can confidently say that your language came from ours, as your (american) ancestors were most likely from here or ireland. therefore why do you call it math?!
Okay - here's the real question. Why do you euros call mathematics "maths"? It's infuriating. The short name - "math" - is a collective plural, like "people", that encompasses the field of study. Adding the "s" is redundant. Why do you all do it?
plus, and i don't intend to offend, if you're a sexual tyrannosauras does that mean you're extint in the bedroom?