The Language of Mathematics (35): why 2 negatives make a positive

[thetableswillturn]

Single and couple here represents x and x^2 so when you take x multiply by another x you get x^2 You've just replaced x and x^2 with single and couple in order to fit your example but the overall is example is different to what is actually happening when 2 negatives are multiplied together.

[thetableswillturn]

2 ex singles can be thought of as -x^2 that's true, but, couple and single are diferent things. You may think i've misconstrued something here but i haven't. Example -3 x (-3) is really equal to -3 on a number line but it's absolute value is a positive 9 (+9) because what's really happening is it goes from 0 to -3 then back to 0 then back to -3, but has moved 9 places. This is what MUST really be meant by - x - = + Which is therefore an incomplete explanation. Should be - x - = + absolute value

[thetableswillturn]

Absolute value is different from representation

[hazloasi]

3 OF 3 While standing there you can be facing left or right or you can move forward or backwards. Lets define that facing right is positive and moving forward is also positive, while facing left is negative and moving backwards is also negative. If I tell you TO place yourself at the zero mark, face left, and move backwards 3 steps. What will happen? You will end up 3 units to the right, two negative actions resulting in a positive. Hope it helps!

[hazloasi]

2 OF 3 - For example, if you go to purchase something and it cost $3 more that what you have, but you were allow to take it on credit, well, the merchant needed a way to quantify it. That's how negative numbers were born. With time, other applications for negative numbers were found. For example, to indicate direction. Lets suppose you are standing in a corner and we define it as the zero, the starting point. ..

[hazloasi]

1 OF 3 - I think I can help to clarify the issue, but A bit of history first. Numbers were invented to quantify things, so, in the begining only existed what we call natural numbers (1, 2, 3, 4...), then, a day, our ancestors were faced with the questions of how to quantify the nothingness, thats how the zero was born. Time went on, and another day our ancestors needed to quantify, to say in numbers, when we end up with less than we began. ..

[ofschorchedpumpkins]

What you said about math being like languge using a double negative, blew my fucking mind.

[chychochycho]

Good, because it blew my mind when i realized it as well.

Peace.

[boshea8498]

it may as well be called an axiom. i dont know what a positive is. do two positives make a negative?. we are talking about a human imagined structure system. we are talking about the tao. the coin. if you play a binary logic system it is in itself this idea. it goes with this idea. it is inseparable from. say i have a coin and i say 'to negate = flip the coin over'. now if we double the negative and flip the coin twice then we end up at the starting point which we called positive.

[allegrobas]

Upon further inspection I now conclude that even the math is NOT OK. His explanation is a tautology. I know that math requires that 2 negatives, multiplied, give you a positive, but I still do not know WHY. This video is worse that I thought originally.

[allegrobas]

The math is OK, but the video is a VERY POOR INSTRUCTIONAL TOOL because this guy TALKS TOO MUCH ABOUT stuff irrelevant to the theme at hand. Yech! I gave it a NEGATIVE.

[copperring1983]

Assume a state of change from the earlier event.... at one moment I owed 2 dollars (-2) to 6 people that don't exist (-6). I'm assuming that I need 12 dollars... that I don't have at the moment... and 6 people who also don't exist at the moment.......The opposite of this must also be true.... So when the 2 dollars start to exist.... then 6 people start to exist too.....that one day I have 2 dollars each for 6 people.... so I HAVE12 dollars, that now are with these 6 people, two with each.

[copperring1983]

If I owe 2 dollars (-2), i.e. dollars that right now don't exist to 6 people, that exist, then I owe 12 dolars (-12) that don't exist, to 6 people that exist.

But if I owe 2 dollars (-2) to 6 people that don't exist (-6), then I owe 12 dollars(-12) to who?

And as far as my state of owing continues and non-existence of people continues, in an event, then I don't have 12 dollars that I owe to nobody.

The assumption '-' * '-' = '+' still doesn't make sense.

Stupid though may be.... !

[Beaveriny]

This is false. -i * -i = -1, two negative do not always give you a positive =)

[VellianoRosso]

Cannot agree with this explanation.

It all dependent on your frame of reference.

If u agree that +*+=+ , +*-=- and -*-=+

Then u must also agree that +*+=- , -*+=+ and -*-=-

All that accurs is a shift of your direction (what u want to accomplish).

It is inherently exactly the same.

[Occamed]

I really liked this analogy until we get to 6:04. At which point I think it fell apart. Once you understand the notion of 'and' and 'with' - the idea of a couple going to a party bit was fairly meaningless.

Two people go to a party, sometimes they are a couple and sometimes they are not, probably confuses people as much as anything.

Thanks for your insight though!

[rccaulfield]

Sorry for going back to this but if the fundamentals aren't right in my head i can't respect the applied areas- What observations led to this operation being formed then? For example in terms of debt if you owe 3 dollars to someone(thats -3) and owe 3 other people 3 dollars, then isn't your debt 9 dollars(-9) not plus 9 i mean they would owe you 3 each in that case? I'm not talking about adding up your debt here. I'm talking about multiplying your debt by 3 debts? Robert Robert

[chychochycho]

Sure, 3 times -3 would be -9.

Don't let this confuse you, just treat it as you would in English, a double negative is positive.

[Kevo216666]

I'm pretty sure you can prove anything when you substitute one concept for another. You're either a brilliant or this is bullshit. I'm not sure.

[chychochycho]

Well, it is just an inherent property of the language, and yes, you are correct, you can prove anything this way. This video is not for people who are well versed in the language of math, it's for people who are having a hard time with it.

The simplest answer to this question is given at 1:47 into the video. Just like the English language, where a double negative makes a positive, so it is with math. It's really that simple... the rest of the video is a song and a dance.

[Kevo216666]

@chychochycho Thanks for the reply. I fit in niether category I'm afraid. I came across this by accident. I'm pretty sure I'm out of my depth already. Good luck to all of you - whatever you're on about. x

[kingofdice66]

@Kevo216666 i assure you this is bullshit and has nothing to do with math, that's not a mathematical proof, this is very confusing

[sib0kralj]

bullshit

[DeanBKS]

You are by far a poor mathematician, explainer and have no understanding of numbers, chychochycho.

[SearchBucket]

If some one owes me something (minus), and I take away that debt (minus), its the same as adding the same amount :-)

[ScottishProfessor]

perhaps some of those new concepts that were discussed in the video? See my two short, incomplete (just shared the core concepts for now) videos "Negation Negated" and "Spherical Math."

[philomath34]

I tried to download your torrent file- it said I had to be logged on to your website? Any suggestions?

[chychochycho]

you don't need to be logged into to my site to download the torrent. Trying going to "the pirate bay" and doing a search for "chycho" ... the three torrents should show up. No logging in required.

[220Rachel]

omg like over half the video he talks about why he hast answered it and when the person asked it and everything but answering the question.. it frustrated me

[gabrielabianca]

when u multiply x by 2(double it) you say u have 2 xs , wen u multiply 3 by 2 u have 2 3s , 2 3s is just like 3 plus 3 , witch ecuals 6 , when u multiply a negative number lets say -2 multiplied by 3 (u triple it , you'l have 3 (-2)s that means -6 , i think this is a reasonable explanation over "why does plus multiplied by minus ecuals negative , i want and explication just like this when u multiply a negative number with a negative number .

[315Doug]

one "AND" one equals two....

not "one"

[seemangal123]

I dont think that you heard what he was saying ,neather what he was wrighting on the board. I will use this to help you this to help you ( please keep in mind that math is a LANGUAGE BY IT SELF ok ) e.g integers -7 -- (-2) = -7 + (+2) = -5 thou this is not the thing but can help you to grasp towards it .a single 1 will = ( -1 ) a couple / two ,let us say it is complete , because two person can bring forth a child but one person by his or her self canot . got it ? ;-)

[gigagroove]

You're a GREAT teacher, great skills. One teacher to another. Peace from your edu brother in America.

[chychochycho]

thanks brother, and I think "peace" is exactly why we do this.

[trahanp]

Now, think about this one: if multiplying by -1 rotates the number line by 180 degrees, then multiplying by the square root of -1 would rotate the number line by 90 degrees (because the sq root of -1 times itself is -1). The sq root of -1 is abbreviated as "i", or the "imaginary" part of a complex number. But there is nothing imaginary about it. You see, a complex number is simply a 2 dimensional number. Instead of living on a "line" it lives in a vector described by 2 lines: the x and y "axis"

[chychochycho]

thanks trahanp,

love these explanations :)

[trahanp]

Think in pictures. Think of a number line. Multiply it by -1. What have you done? You have rotated the number line by 180 degrees. That is what multiplying buy -1 does. It creates the mirror image, or the inverse, of what it multiplies. 2 negatives make a positive because when you multiply by -1, you invert the number line. I had trouble with algebra until I discovered analytic geometry. Being able to see numbers as objects in space really helps once you get the hang of it.

[loverpeace33]

thanks

[eryksun]

Think about it rationally. For example, -2 = -1*2 = 2/(-1). Then we can say -3 * -2 = -1*3 * 2/(-1). But by the associative property this can be written 3*2*(-1)/(-1). And clearly -1/(-1) = 1 since any non-zero number divides itself once. So -3 * -2 = 3*2*1 = positive 6.

[eryksun]

1 and -1 are just two points among an infinite set with unit distance from the origin (a unit circle) in the set of complex numbers. It's based on a number I = sqrt(-1). I^2 = -1. I^3 = I*I^2 = -I. I^4 = I^2 * I^2 = -1 * -1 = 1 = I^0. But you can also have I^0.5, etc. As the exponent goes from 0 to 4, the point moves continuously 360 degrees around the origin. Every complex number is just A*I^B, given A in [0,inf) and B in [0,4). This also unifies exponential and sinusoidal functions.

[JustinoXProductions]

thats exactlly what thought, when i came towards realization of this i started to do better in math.

[pengbertuuu]

If we define mn by the sum of n m's, define (-m)(-n) as mn and define (-m)n and m(-n) by -mn for all positive integers m and n, then our definition of multiplication has good properties so that it and addition form a ring on integers. Or you can define multiplications abstractly as binary operations on integers so that it and addition form a ring on integers. You may then prove that (-m)(-n) = mn for all positive integers m and n.

[virushaters]

tnx..

[virushaters]

101-10 to the power of two=1

[chychochycho]

haha cool,

101-10^2 = 1

i like it :)

[virushaters]

can you answer this....pls...

move one digit to make the statement true....

101-102=1

[chychochycho]

okay i give, how do you do it?

[eiriker]

haha

According to you this would be true:

A single (-1) goes to a party with a couple (+1):

-1 + 1 = 0

Ergo: nobody goes to a party.

[mentor32]

I think the language of maths is not taught enough. I can tell you're very passionate about maths and when you explain other things on your videos, you do it effortlessly. This makes me think that the language of mathematics, is much more harder to explain. I don't agree with Deanbks, coz u have helped a lot of people with your vids and what has he done. Thanks bro.

[Ijustwanttoseevideo5]

OK I get the logic of your argument but I'm still not sure why two negatives equal a positive because it seems to me that they way numbers should work is that both the negative and positive number lines should be symetrical so that two negatives make a negative and two positives make a positive. I'm not sure how combos would work though. I think the question I am asking is why the positive and negative number lines are not symetrical.

[Kobulingam]

There is a property of our number systems called the distributive property:

a(b+c) = ab + ac (left distributive)

(a+b)c = ac + bc (right distributive)

These are true for positive numbers, and if we WANT THEM to be true for all numbers, we require that two negative numbers multiply to give a positive number. This is the ONE AND ONLY reason for it.

[csikjarudi]

You got that right!

[DeanBKS]

You obviously do not comprehend a proof-maybe glance over principia mathematica before posting such obsurd videos claiming to dispel doubts.

[chychochycho]

Hello DeanBKS,

this video is not about proving that a negative and a negative equals a positive in the language of mathematics. It is about explaining that mathematics is a language, and that a negative is a property of a number.

If you are looking for a proof that - * - = + than just do a quick search online. There are many sites that use the language of math to prove this.

hope that helps :)

[DeanBKS]

The demonstration above is by far the most illogically derived and mathematically void I could have imagined. You cannot simply write down to a question 'neg.neg=pos' well I know that -1.-1=1. This is in effect what you did with the couples analogy-yet ten times worse as the use of single and couple was simply crazy. i.e. you effectively stated let A=-1 and B=1. A.A=B. The use of couples or singles to back it up does not give any ANY kind of support to the example, maybe only slight of hand.

[chychochycho]

see above comment.

[DeanBKS]

Videos like this are a waste of time, and really discredit the beautiful language of mathematics. POST NO MORE.

[chychochycho]

oh i definitely agree that math is a beautiful language and i definitely do plan on posting many more such videos.

[AmigaFalcon]

DeanBKS: I think the sheer volume of positive comments which Chy receives are "proof" that his unique style of explaining mathematics is of great value.

Many roads can lead to Rome, not just yours. If you were a little wiser and less ego-centric, you might realize that fact.

Anyway, I'm really looking forward to DeanBKS's Principia Mathematica YouTubius videos, which demonstrate the "correct" and "classical" way to teach math. Something tells me I'll never see those though.

[bello787878]

thank u!

[AmigaFalcon]

Very interesting, as always! Made me think about numbers in a way I've not really considered before.

Really looking forward to your new batch of vids!! :) Thank you chy!

[CousinoMacul]

"Two negatives makes a positive" is true in multiplication, but not in addition (example from English: "No, no!" means 'double no') [addendum: I see you covered the addition/multiplication issue in your video.]

The example I use when I'm asked the question, is:

Suppose you're facing backwards (negative), then turn to face backwards from the way you're facing (negative operation), you'll be facing forwards (positive).

That's my take.

Nice video!

[party12345]

Based on your example: "Matt and Sara go to a party". Now the statement does not imply that they go together as a couple . yet the "and" would give us a value of "+1" - Simple to say Math and English can be incompatible at times.

[chychochycho]

haha true, but then again, they could end up becoming a couple. Neither Math nor English are complete, and very seldom is something perfectly translated from one language to another. Definitely an accurate statement, "Math and English can be incompatible at times."

[wumby]

Nice.

Very well said!

"A new language"... fascinating!

[terryphi]

Wow! 7th grade now makes sense! thanks so much! this was very creative and innutive.

[nairb978]

What if there are two single people with benefits? [(-1+-1)/2]^2?

[Ezcut]

nice job