[Closed] maths poser from my 12 year old - why is -1 * -1 = +1

(-3) * (+3) = +9

err,

isn't it -9?

minus*minus = plus
plus*minus = minus

Google is your friend [url= http://mathforum.org/dr.math/faq/faq.negxneg.html ]Explanation[/url]

Surely the answer is "it just is, ok?", followed by a slap round the back of the noggin. 😀

wwaswas ,

typo - sorry

will read that mefty,
a mate has also just pointed me at http://en.wikipedia.org/wiki/Distributivity

and it's root, not route, just FYI.

wrong he said it was '+/- 3' which is quite correct.

Actually there are [b]four[/b] fourth roots: +3, +3i, -3 and -3i, where i is the square root of -1.

Hope that helps 😉

Two wrongs make a right, two negatives make a postive 🙂

I like the statement in that first link

This convention has been adopted for the simple reason that any other convention would cause something to break.

cheers elliptic, you smart allec, you are reminding me of things from way back in my degree that I would rather forget. Z planes noooooooooo

I've just done a load of calculations to model sonic flow in pipework, and I'm at a loss to give a simple explanation.

It just does?

Reminds me of the teacher in Glasgow trying to explain that two negatives make a positive, but two positives cannot make a negative.

Pupil resonds "Aye right!"

😆

woody2k +1

How about this (overly simplified non-maths) explanation:

Negative "means not having something" or "taking away", positive means you have something.

So, -3 x 5 means you are taking away 3 of the fives I have, so that's -15 in total.

A double negative -3 x -5 means "taking away the taking away", so you are giving.

Then of course -1 x -3 x -5 means you are taking away the...

Oh **** it, I've confused myself now.

Some things are the way they are by definition. It's maths, not physics - so we get to make the rules.

OT, I know, but it puts me in mind of this joke:

A mathematician, a biologist and a physicist are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty."

I think Grahams has the best answer. take it back to waht happens if you have 2 lots of 3 3 lots of -2 then -3 lots of -2 (ignore ones as they make things less easy to understand in my opinion.

This convention has been adopted for the simple reason that any other convention would cause something to break.

Well I guess its proof by contradiction or Reductio ad absurdum.

try him with .999 (to infinity) = 1

Always a favourite.

I always like the definition of the sciences I was taught:

If it moves it's biology
If it smells it's chemistry
If it doesn't work, it's physics
And if you can't understand it, it's maths.

Obligatory xkcd (with octopus!):

[img] [/img]

It is all to do with the basic axioms of Field Theory. Let F be a field and let a be an element of F.

Then there exits an element 0 such that a + 0 = 0 + a = a, and an element 1 so that a*1 = 1*a = a and for each a there is an element -a such that a + (-a) =0 and the inverse of a, 1/a such that a * (1/a) = 1.

Therefore, if a is an element of the Field F, then there exists and element -a, and therefore (-a)*(-1/a) = 1.

25 years since I did such stuff at Uni so this may not be quite right but the basics are there. Now if you want to know about the Primary Decomposition of Noetherian Rings I might be your man!

GJP - Member
It is all to do with the basic axioms of Field Theory. Let F be a field and let a be an element of F.

Then there exits an element 0 such that a + 0 = 0 + a = a, and an element 1 so that a*1 = 1*a = a and for each a there is an element -a such that a + (-a) =0 and the inverse of a, 1/a such that a * (1/a) = 1.

Therefore, if a is an element of the Field F, then there exists and element -a, and therefore (-a)*(-1/a) = 1.

Jesus, lost me after let F be a field lol

Let F be a field

[size=5]F = [/size][img] [/img]

let a be an element of F

[size=5]a = [/size][img] [/img]

Right.. with you so far...

Hang on, isn't the inverse of a field, a road?

Inverse of a field is the sky?
Will the maths above help me decide which new bike I need to buy?

Come on guys your all bright chaps its not that difficult to follow.

molgrips summed it up pretty well really

[i]molgrips - Member
Some things are the way they are by definition. It's maths, not physics - so we get to make the rules.[/i]

I think part of the problem is that we are all taught at school about the four basic mathematical operations addition, subtraction, multiplication and division. We have all been conned, in a strict mathematical sense, subtraction and division do not exist.

I'm not sure it's so easy to argue that maths has no basis in the physical universe. Clearly it does in basic additions etc.
It also appears to in more abstract concepts like imaginary/complex numbers. Many physical systems need complex numbers to be described properly.

We have all been conned, in a strict mathematical sense, subtraction and division do not exist.

Indeed. If you have five apples and I take one, then I haven't actually subtracted an apple. That would be silly. I've just added one additional negative apple. 🙂

[i]GrahamS - Member
We have all been conned, in a strict mathematical sense, subtraction and division do not exist.
Indeed. If you have five apples and I take one, then I haven't actually subtracted an apple. That would be silly. I've just added one additional negative apple. [/i]

Exactly. I know in our day to day dealing with our various number systems, be it integers, fractions, and real numbers etc, then subtraction and division are intuitive concepts and I wasn't for a second trying to suggest we do not teach our children in this way. Although, I have no strong or qualified opinion on the matter really.

But if my fading memory serves me correctly there is not an "algebraic representation system" that I am aware of that includes the operators subtraction or division (Groups, Rings and Fields etc)

Indeed. If you have five apples and I take one, then I haven't actually subtracted an apple. That would be silly. I've just added one additional negative apple.

how many negative apples did you have to start with?

-0 of course.

Not read much of this but does anyone actually need to know this on a day to day basis, because i don't. 😯

I know in our day to day dealing with our various number systems, be it integers, fractions, and real numbers etc, then subtraction and division are intuitive concepts

Not in my day to day. I'm a programmer so I know that

[code]1 + 1 + 1 = 11
 
DEAD + BEEF = 19D9C
 
6.1 = 6.099999904632568359375
[/code]
😀

[i]GrahamS - Member
I know in our day to day dealing with our various number systems, be it integers, fractions, and real numbers etc, then subtraction and division are intuitive concepts
Not in my day to day. I'm a programmer so I know that

1 + 1 + 1 = 11

DEAD + BEEF = 19D9C

6.1 = 6.099999904632568359375
[/i]

All seems perfectly intuitive to me 😆

Whether base 2 or base 16? (I assume the second example is hexadecimal) the principles are the same

Yep, binary, hex and [url= http://en.wikipedia.org/wiki/IEEE_754-1985 ]IEEE floating point[/url].

The last one being a source of many, many, many bugs and confusion over the years, as basically it is a system where you can never rely on exact floating point values (1.0 + 5.0 == 6.0 is true, but 1.1 + 5.0 == 6.1 is false!) so all you can ever do is make sure they are [url= http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm ]almost equalish[/url] 🙂

OK so much like this math stuff i learnt the basics of binary at school..... never used much of that either, but the hex and IEEE seems a bit specific - do you do this for a living? 😀

If it doesn't respond to the liberal use of a hammer, then stick ya tongue out and hit it harder!

🙂 😀 😆

NOTE: not ya tongue!

the hex and IEEE seems a bit specific - do you do this for a living?

'fraid so. 😳

Funnily enough though I have always been fairly crap at maths. But computers I get 😀

Oranj - Member
OT, I know, but it puts me in mind of this joke....

when challenged by my very non maths better half (who excels in other fields by a wide margin)that i really do understand maths i usually deny it - but i did laugh at that joke!

Roots are easy if you thinking polar coordinates..... if anyone cares I'll dig out a quick explanation, but polars are awesome for explaining stuff.

polars are awesome for explaining stuff.

[img] [/img]

[i]Now if you want to know about the Primary Decomposition of Noetherian Rings I might be your man! [/i]

Isn't that caused by too much bum sex?

He won't need to know any of this to get 3 stars at McDonalds

Try to take it out of the maths context:

"I am going..." = Positive
"I am not going..." = Negative

Here's how it works:

"I am [i]not[/i] NOT going..." = Negative * Negative = Positive

If you're not, "not going" then you're going. Hence, positive. This is how I explained it to myself some years ago. Dunno if it's right or not but it beats pages of mathematical proof.

The really awesome thing is that now we're past 41 posts the title on the forum page reads:
"maths poser from my 12 year old - why is -1 * -1 = +1 - 2"

keep it simple

3 * 4 = 12 [center]-4 * 2 = -8[/center]
2 * 4 = 8 [center]-4 * 1 = -4[/center]
1 * 4 = 4 [center]-4 * 0 = 0[/center]
0 * 4 = 0 [center]-4 * -1 = 4[/center]
-1 * 4 = -4 [center]-4 * -2 = 8[/center]
-2 * 4 = -8 [center]-4 * -3 = 12[/center]

All about patterns when you look at it. (go down the columns not across BTW).

HTH

-4 * -1 = 4

It was OK up until that point in my non mathematical brain.
Anyway havent the bankers been using the two negatives = a positive up until recentley ?

1 * 1 = 1
(2 - 1) * (2 - 1) = 1
4 - 2 - 2 † ( -1 * -1 ) = 1
-1 * -1 = 1

off course there's a few more assumptions in there

I never understood how you could calculate the area of a circle using PI since PI is an unknown quantity.

In calculating the area of a circle with a radius of 1 - the the area would be:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................................. to infinity and beyond!!

PI is an unknown quantity.

There may be formulas for calculating Pi but all the digits for Pi haven't been calculated yet....... will they ever be? My point is if you use Pi to calculate the area of a circle you'll get an indefinite string of numbers - not very accurate!

all the digits for Pi haven't been calculated yet....... will they ever be?

if you use Pi to calculate the area of a circle you'll get an indefinite string of numbers - not very accurate!

OK, so you might argue you want an accurate mathematical answer - the thing is, a mathematician would say that the area of a circle radius 1 is pi (they're not really into numbers)!

In calculating the area of a circle with a radius of 1 - the the area would be: 3.1415926535...

but how would you know what the radius was ? By the time you've measured it, some of the vernier has rubbed off...

as a professional measurement geek i'm loving the way this thread has gone!