Why is a negative number times a negative number positive❓❓

[@paulmcateer]

By removing some negative comments to this video you are left with the positives

[@michealmorrow1481]

I really want to see this demonstrated on a number line.

[@markmarkus808]

How to do this with apples

[@ItsLinaH]

Here is another cool explanation demonstrated on a number line ☺ One of my favourite explanations kzbin.info/www/bejne/f4W2e4WliNOZj68

[@michealmorrow1481]

Unfortunately, you fell into the same illogic that others have fallen into. At one point, you assume the answer is 4 by using the very thing you are trying to prove, before you proved it. That is wonderful illogic! Really, try not to do that and post a video which does not rely on false use like this.

[@ItsLinaH]

Yeah sure, I didn't make this video, I just thought it was a good explanation

[@kulen8704]

kzbin.info/www/bejne/i2PdfaKKfJuJfLs

[@Dazzletoad]

Yeah now I'm even more confused.

[@petearvo8918]

Try this method I attached. kzbin.info/www/bejne/i2PdfaKKfJuJfLs

[@tEqUiko]

😂 kzbin.infohBS63AVi42g?si=kRa0R9TKEjhqITK5 🤔🙄

[@tEqUiko]

kzbin.infohBS63AVi42g?si=kRa0R9TKEjhqITK5

[@alittax]

5:43 I'm not sure if this counts, but: if you turn around twice, you're facing the original direction again (2*180=360). Or: if you add two odd numbers, you get an even number.

[@misaltas9499]

Cool video! Let's take a word, pineapple, by reversing: alppaenip Another one: pen -> nep Now 2 concatenated reversed words: alppaenip nep -> alppaenip nep are 2 concatenated reversed words. I wish they were 2 concatenated "normal" words but it doesn't work hahaha Maybe it's easier if you think in two light switchs connected, turn off the light in each switch is the same as turn on the light

[@discovermaths]

I like your idea of using light switches! They could be wired up to show the rules for combining signs just as a computer consists of many switches for doing calculations.

[@coding-rabbit]

THX i really like your content! NICE JOB S2

[@geochum]

Awesome explanation!

[@rahillhazari1692]

electron itself is negative charge when the reverse direction of direction of motion of electron is taken to account, the current comes out positive

[@podometic]

Please start with a formal axiomatic definition of multiplication. As per Aristotle, you can't introduce undefined terms in a proof. Thank you.

[@angelmendez-rivera351]

He did that in his first video.

[@manuelzaldivar5656]

So why aren’t two positives a negative

[@manuelzaldivar5656]

I forgot I commented this once thank for reminding me a month later

[@sagnikdhar7073]

the "less and less" marks you get in your exams the "more" beating you get at home..... :-)

[@0xTRellyx0]

This doesn't clear anything up.

[@angelmendez-rivera351]

Too bad.

[@Happy-qd3yb]

I feel like I understand math finally. We decide the true statements and prove everything else from there. So technically we decide what should and shouldn't be allowed in math so we technically should allow ourselves to bend math somewhat to our will. Like maybe 1 should equal 2 but only when we divide by zero because that's how math is supposed to be and how we already have been building it

[@raghunath97032]

Irrational quantities like root(2).root(3)=root(6)

[@magilas8485]

Its because if you rotate the other negative sign by 90deg then put the symbols together, you get a + symbol

[@rakeshchinnakar6599]

May be Adding any 2 natural numbers

[@happy543210]

that was clear as mud.

[@angelajackson7560]

I zoned out, all I heard was negative A........... blahblahblahblah

[@angelmendez-rivera351]

@@angelajackson7560 That is your fault.

[@angelmendez-rivera351]

I think the way symbols were used in this video is too confusing for an audience that is already confused about why (-1)·(-1) = 1. Here is a better way to understand what is happening. By definition, 1 + (-1) = 0. Since 0·0 = 0, it follows that 0·0 = (1 + (-1))·0 = (1 + (-1))·(1 + (-1)). Here, we can use the axiom of distributivity, which defines what multiplication is, so (1 + (-1))·(1 + (-1)) = 1·1 + (-1)·1 + 1·(-1) + (-1)·(-1) = 1 + (-1) + (-1) + (-1)·(-1) = 0 + (-1)·(-1) + (-1) = (-1)·(-1) + (-1) = 0. However, notice that 1 + (-1) = 0, so (-1)·(-1) + (-1) = 1 + (-1), which means (-1)·(-1) = 1.

[@plazmaguy13yago9]

5:02 seriously? Negative times a negative is positibe because i said so

[@fakharzamanzaman983]

Not sure, but we can solve this Delmar by using our daily life words. if i say it is raining and you also say that it is raining. it is actually raining than it is +ve x +ve = +ve. if I say it is raining and you say it is not raining, but it is raining than it becomes -+ve x -ve = -ve. if we both say it does not raining than it will become -ve x -ve = +ve.

[@jackbotman]

Yup, this is why so few people like math

[@akashvivo3323]

Sir what guarantee that negative no times negative no even follow distributive laws. Truth of laws such as distributive is only judged after the arithmetic operation is well defined intuitively but u are using a property when even the arithmetic operation doesnot makes a sense

[@angelmendez-rivera351]

No, you are incorrect. Operations are _defined_ by axioms that they satisfy. The axiom of distributivity is the definition of multiplication.

[@mohso2001]

if 2*2=2+2=4 why -2*-2=-2+-2=-4 not 4?? note: definition of multiplying is repeated Add

[@hollybobie8144]

Its because even though you get the same product with 2x2 and 2+2, multiplication is a notation of addition. This means that the 2 in the front of 2x2 is simply saying there is 2 groups of 2 and we are adding those groups together. Meaning, that if you are doing 2x-2 what you are really saying is -2+-2. Think of it with different numbers: 3x2 means 3 groups of 2, or 2+2+2 and 3x-2 is 3 groups of -2, or -2+-2+-2. I hope this answers your question.

[@robthomas8335]

This is why I fell asleep in high school.

[@puttputt524]

I would like to say your proof is great for Algebra heads. But I am not...

[@vansf3433]

Ex: 2 x 6 = 12----> 2 = 12/6 But 2 x 0 = 0----> 2 = 0/0, which is obviously nonsense, although we follow exactly the same steps as the above arthimetic operation. Whenever you try to multiply or divide by zero , the only correct answer is undefinable due to the fact that zero DNE

[@EducationNextOfficial]

?????? #EducationNext

[@kaushaltiwari9608]

Could've explained differently and easily

[@Happy-qd3yb]

No you cant

[@angelmendez-rivera351]

@@Happy-qd3yb Yes, you can, using distributivity.

[@Happy-qd3yb]

@@angelmendez-rivera351 can you show me please but spread it out very clearly

[@angelmendez-rivera351]

@@Happy-qd3yb 1 + (-1) = 0 This equation defines what -1 is/does. Square both sides of the equation (1 + (-1))^2 = 0^2 0^2 = 0, so (1 + (-1))^2 = 0 Write the square as a product (1 + (-1))·(1 + (-1)) = 0 Use the axiom of distributivity (1 + (-1))·(1 + (-1)) = 1·(1 + (-1)) + (-1)·(1 + (-1)) = 1 + (-1) + (-1)·1 + (-1)·(-1) = 0 1 + (-1) = 0, so 0 + (-1) + (-1)·(-1) = (-1)·(-1) + (-1) = 0 1 + (-1) = 0, so (-1)·(-1) + (-1) = 1 + (-1). Both sides of the equation have a (-1), so you can cancel it out (-1)·(-1) = 1. Q. E. D.

[@Happy-qd3yb]

@@angelmendez-rivera351 I'm not a mathematician or anything but how do you go from 0+(-1)+(-1)•(-1)=(-1)•(-1)+(-1)=0 To (-1)•(-1)+(-1)=1+(-1) But the (-1)•(-1) was turned to 1 even though we haven't proved that yet.

[@catirerubio]

This boils down to memorizing the steps. a negative times a negative equals a positive makes no sense to me. If I withdraw $10.00 times $10.00 from my bank account, the account is $100. less. Sure, I have plus $100.00 in my pocket, but not in the account.

[@MrsUnderhill-yz1pv]

You do not withdraw it ten times (that would be -$10 x 10) you need to undo the withdrawing of $10 ten times (-10 x -10). That is exactly the same as putting $10 to your account 10 times just very intricately expressed 🙂

[@catirerubio]

I do not understand that explanation, at all. but thanks for taking the time trying to explain it. @@MrsUnderhill-yz1pv

[@whitehairedbadass3475]

​@@MrsUnderhill-yz1pvperfect explanation of that

[@bradkalbfleisch5379]

Double Entendre.

[@markmarkus808]

Entendre=to hear. 2xentendre=two hear stereo. Sorry Dave Thomas

[@kentjordan4658]

too complicated

[@Spaniards56]

No explanation is enough to make it clear. Just keep saying negative times a negative = positive. Do not waste more time trying to understand it unless there is someone capable of doing so.

[@alimranahmed4116]

The audio is horrible.

[@dakshdudee2278]

Heheh 😄

[@Jason-yq9lq]

LoL the product of negative sheep x a number of negative sheep somehow you have all them positive number of sheep, PASS THE DUTCH W YOUR LEFT

[@vittyiebin8362]

Negative multiplies by a negative is equal to a negative to me but if you clarify it as a positive the world will go bankruptcy for sure.

[@whitehairedbadass3475]

Nah you're thinking like addition Think of it as a double negative in a sentence. If your first sentence is "I am happy" + Then "I am unhappy" - Then " I am not unhappy" - -. ( Just means i am happy) So the double negative just circles back to positive.

[@madhavsanap6690]

Not intuitive

[@darringodden7225]

Well you sure did twist my melon with this. I was only wondering why 0- (-3) =3,I thought it was because the -& the -cancelled each other out. Oh well back to my times tables (I am only 57)

[@srinu57]

No body has proved this on the number line so far

[@lisasnortum-phelps5458]

I found 2 examples, same idea: kzbin.info/www/bejne/i2PdfaKKfJuJfLssi=f5IgHI2xOsbapE52 and kzbin.info/www/bejne/mWaTmnugoMl5etEsi=nDICXJStVJbvHPNT

[@kazedcat]

The number line is not a fundamental axiom of mathematics. The number line only exist after constructing the set of real numbers. But negative numbers are constructed to form the set of integers. So number lines are form after Z×Z but negative numbers are form after N×N.

[@sxenonomania-1882]

Two student study,s everyday 6 hours, And two student everyday study 2 hours, and play 2 hours, and these two got more marks than those two, There u got the example of real situation mathematician, It could also be example of Smart work vs hard work..

[@felren13]

i want to buy it...really! but i don't because, just because you said something earlier doesn't mean you proved it earlier, which as far as i followed, you didn't prove it earlier so its not proven later. this issue, not you, is really annoying me. no one seems to, in my mind, make this stick. its looking to me that this is a common issue exactly because its false. its got to be sold because its not true...

[@angelmendez-rivera351]

You are employing the classic "I don't understand it; therefore, it's false." You must be a flat Earther. Try to understand it first before you try to deny itz

[@vansf3433]

At the step (-a) *(-b) + (-a)* b = 0 ---> -a(-b + b) = 0, you tried to hide or cover up the fact that the negative sign of the left side carried by a in the ambiguity of the variables You can never have the same variable with two different or opposite values at the same time. In your misleading and ambiguous example, you claimed that b can be both positive and negative at the same time, which is obviously absurd You can assign only one value to a variable each time, but you can never assign 2 opposite values to it at the same time. In + b , the positive sign + indicates that b is an increase in scalar value to be added to a quantity. Oppositely in - b, the negative sign indicates that b is a decrease in scalar value to be taken away from a quantity. Hence, they are completely different, or as what you call them as the 2 opposite values. you can assign and use either positive or negative sign to the variable b separately at 2 different times, but you can never assign both positive and negative to it simultaneously while the positive sign and negative sign represent 2 opposite meanings Let + b be defined as being male, and -b be defined as being female Now, you can be either +b which male or - b which is female, but you can never ever be both + b and -b or both male and female at the same time as the ambiguous way how you tried to define the variable b In computer science, such ambiguous languages are taboos because unlike humans, computers and AI do not understand any statement which carries 2 meanings. You would be very bad at programming if you ever tried to learn one, and apply such ambiguous languages Your nonsensical and fundamentally mathematically incorrect, or contradictory statement here can be mathematically expressed like this: If b < 0 ( negative)---> b > 0(positive) Or let b = turn on the light , - b = turn off the light b = turn the light off = turn the light on You can either turn the light on or turn the light off , but you can never ever both turn on and turn off the light simultaneously, as your nonsensical claim + b and - b could exist at the same time.

[@vansf3433]

I'm 100% sure that no human mathematician can ever prove such nonsensical notion of mathematics invented by human ignorance of their own invented concepts of mathematics because human subjective interpretations are always objectively incorrect

[@nathaniel-TV-project]

It is really indeed burdensome to draw the line between what is subjective and what is objective. However, the mathematics that you call "nonsense" is the very same mathematics that made it possible for you to produce digital content like the comment that you posted here. Bertrand Russell once said that mathematics and the scientific method is more of like an approximation that allows us to get closer to what is objectively true but the question on whether it describes the universe can be answered by just looking at the technological progressions that humanity has ever made as well as the increasing understanding of the world around us as well as physical phenomena. I'm not sure if mathematics is truly objective or not because even the concept of objectivity can be quite limited only to what we humans are able to perceive with our brains. But I think this is what makes mathematics so thrilling to pursue and explore because there is a lot of mystery behind its effectiveness in describing the world around us. If you look at the perception of the mathematical community when it comes why mathematics is effective, it is also a mystery for most of them. And this mystery is what stimulates curiosity that eventually lead to new ideas that will propel our understanding of the universe and the progress of humanity even further.

[@simpleman283]

I was going to give this video a 👎, but I noticed I already had.

[@whiskywillie]

Just take it at face value...no proof required lol

[@giannirussso]

Some people value evidence, logic, and explanation more than others, as is apparent by your comment.

[@vansf3433]

First of all, negative numbers and zero never ever actually exist anywhere else in the universe other than human wild imagination for you to perform any sort of arithmetic operations with such non-existent values You can apply arithmetic operations with quantity values which exist in the real physical world, and can represent a form or different forms of matter in the real physical world. But you can never actually do so with such non-existent values as negative numbers, including negative infinity, and zero You can show me 2 books of mathematics, but you can never ever show me negative 2 books of mathematics, nor zero or 0 book of mathematics simply because negative numbers and zero DNE for you to show any of them. They are unreal or merely imaginged by humans extremely limited knowledge Can multiplying a £20 in your pocket by such a non-existent value as zero will ever actually result in zero or no or 0 £ in your pocket? The answer is obviously no, never ever at all Can you ever actually multiply such a non-existent value as a negative number by your £ 20 to result in a negative amount of £s, say, negative 5 , and the resultant products will be negative £100? The answer is obviously no never ever either So, negative numbers and zero DNE, and therefore you can never ever actually use them in any mathematical operation Secondly, you have merely presented here a sort of circular argument, in which you used your unproved claim as a fallacious proof for your subjective statement, without proving at all what you have to prove. All what you have done is to apply such unecesserily lengthy mathematical manipulations just to prove such an obvious fact which everyone already knows, as a negative quantity value when added to an equal value with a positive sign will result in 0 or zero, while you have never ever been able to prove : How can it be possible that (-) x(-) = + on the left side, and -(-) = + on the right side. All what you have actually done here is to try to move negative signs into and out of the parentheses, and prove that a negative quantity + an equal quantity with an positive sign=0, and just jump to the conclusion without any valid evidence