I’m DONE with Minus Signs

[@WrathofMath]

Let me know if you really wanna learn about multiplication and division in negative bases, I prepared notes on it but in the end I didn't think it was interesting enough to be worth the time. Join Wrath of Math to get exclusive videos, lecture notes, and more: kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin More math chats: kzbin.info/aero/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO

[@veganwater381]

I would love to! And also, is there a way to represent 0.99... in negadecimal? Does it involve imaginary numbers? Like 0.90..I + 0.09..?

[@AstaryuuGaming]

@@veganwater381 To convert the decimal component to negadecimal, every other place value starting with the tenths place increases the number to the left of it by 1 (if it is 9, it goes to 0 and subtracts 1 from the place to the left of that) and then is replaced by 10 minus itself. Therefore, 0.999... becomes... 1. Just 1.

[@MichaelPiz]

Your theme song for this video is obviously "Too Much Time on My Hands" by Styx. Also, you edited in the same audio snippet of the word "negadecimal" everywhere it appeared in the video, didn't you? That's effin' hilarious and proves that the song applies _hard._ Also also, you introduced an _i_ at 20:38. That's just _mean!_ Finally, you said early on that we can use _any_ number for a base. Oh yeah? Show me base _i,_ smart guy. 😁 P.S. I had commented two of the above quips separately in replies here but they disappeared. Let's see if this reply survives.

[@dontuserachelslurs]

Oh wow that's way easier than writing a small horizontal line

[@shennyboi110]

😂😂

[@rainerzufall42]

Sarcasm detected.

[@Tostermz]

“i realised there’s one big problem, and that is the country of canada and it’s ten provinces.” greatest maths video of all time

[@MichaelPiz]

Ah, Canada. That giant suburb of the Arctic Circle.

[@error_6o6]

if y’all (the viewers) think this is crazy wait till you find out about base 1+i. Yes, it is literally a complex-valued base.

[@SimonClarkstone]

Or base Phi - looks like binary but there can be no adjacent 1s, and IIRC all integers are palindromes with the units place at the centre. If you don't like the inconvenient integers, you can approximate it using the Fibonacci numbers instead of powers of Phi. Even a matrix can be used as a base. All you need for your base is exponentiation (or similar function) by an integer, multiplication of that by an integer, then adding up load of those.

[@ChessTopia]

Is not 1+i , it's 1×i

[@wyattstevens8574]

Or -1+/-i? Combo Class reveals that this (that being either Gaussian integer with a magnitude of sqrt(2) and real part -1) is almost like "Gaussian binary!" ("Gaussian integers," in case you didn't know, is a name for numbers a+bi where a, b are in the ring Z)

[@TonboIV]

A truly wonderful solution! If only we could find a problem for it to solve!

[@WrathofMath]

🤣

[@gary.h.turner]

You used an awful lot of minus signs in your attempt to eliminate the use of the minus sign! 😂

[@Salsmachev]

Yeah I feel like he didn't quiiite give it a fair shake. To do a negative carry in negadecimal addition, just add 19 instead of subtracting 1.

[@merhaba3621]

You can also use a 10-adic number system

[@WrathofMath]

still need to work on this plan 😂

[@damianzieba5133]

​@@merhaba3621 and deal with x*y=0, x=/=0^y=/=0

[@a_capitalist]

2:16 2:42 2:52 4:08 4:30 4:37 6:00 7:21 7:31 7:42 7:48 7:54 7:59 8:20 8:29 9:56 10:12 10:14 10:48 12:33 13:03 13:12 13:22 13:30 13:41 14:56 15:19 16:07 16:31 16:32 17:53 17:58 18:11 18:21 18:29 18:40 18:47 18:57 22:42 22:51 23:04 26:47 27:24 🤨📸

[@WrathofMath]

😬

[@regulus8518]

it would have been way funnier if instead of using a stupid robot voice, you just asked a black friend to help you with this project 🤣🤣🤣

[@txikitofandango]

1:45 nope it's 18 + 6 + 1 :)

[@TheRandomPersonOnYoutube]

Yeah I kinda scratched my head on that one because I know 13 in base 10 is 111 in base 3. He probably just forgot to multiply the number to the power of the base

[@BigFellaDj]

thank god im not the only one who noticed

[@2wr633]

@@TheRandomPersonOnKZbin i think what he forgot is the fact that he was talking about 221, as it seems like he just decided to add them up for no reason

[@TheRandomPersonOnYoutube]

@@2wr633 I guess.

[@TheRandomPersonOnYoutube]

​@@2wr633I guess it can be true. Forgetting the numbers in their respective digits and just thinking about the sum of the exponents is a common mistake especially for me.

[@JR13751]

Problem with negative bases is that carry is 2 digits. John Colson's Negativo-Affirmativo Arithmetik is better. It uses digits from -4 to +5. Edit: Carry can be one digit if it is negative.

[@Hexa1296]

ah yeah, i usually call it signed decimal or balanced decimal

[@thierrypauwels]

Balanced numbers benefit from an odd base. 10 is not really a good base. With an odd base, rounding a number is merely removing the excess digits.

[@rzeqdw]

> There's one big problem, and that is the country of Canada I've been telling people that for years and nobody believes me!

[@Phyrior]

Dude... I know April Fool's Day is amazing, but can you at least hold off until the actual day? I swear, they're making holidays closer and closer...

[@J7Handle]

Why are you unable to say the word negadecimal?

[@StylishHobo]

What do you mean? He said it like 100 times. That's 100 times in *NEGADECIMAL*.

[@ichimiustin8390]

He reused the audio for some reason

[@davidmurphy563]

I suspect he pronounced the first e and an i... Let's, um, not go there.

[@AstaryuuGaming]

The prefix "nega-" is pronounced the same as the N-word (no hard r) for some English speakers, and even for those that don't do that, the words are so similar sounding that it's better to be safe than sorry.

[@eduardoxenofonte4004]

@@AstaryuuGaming i'm pretty sure he was just doing it for the funny

[@LumberLopper]

Did KZbin not like using "nega-" as a prefix and it tried to interpret it as another word?

[@KingGisInDaHouse]

what other word are you thinking of. Please say it so we all know exactly which word you are talking about.

[@StylishHobo]

Nega, please.

[@LumberLopper]

@@KingGisInDaHouse [redacted]

[@gary.h.turner]

Would nega-racism be hatred of your own race? 🤔

[@AstaryuuGaming]

Could be more than just a YT issue - for some American (meaning the American continent, not the USA) speakers, they literally sound the same

[@elunedssong8909]

I thought about this idea before! My solution was have negative numbers every other number. so 100101 is 10^2 -10^1 + 10^0 This makes us use twice the space to represent all numbers, though. Major downside, but addition still works the exact same. And multiplication / division you need to carry across 2 places instead of 1, which is a very simple/ intuitive change.

[@Bengalnoestimido]

Hmm if you take this idea but represent it in base 20, it would take up no more space than in decimal... i think?

[@elunedssong8909]

@@Bengalnoestimido Interesting idea, I can't figure out how to make it work.

[@RonuPlays]

Just as I was looking into bases with negative numbers this video pops up! Please do balanced number systems next (like balanced ternary), I find them fascinating!

[@WrathofMath]

Perfect timing, I will!

[@thierrypauwels]

To remove the need of a minus sign to represent negative numbers, by far I prefer the balanced number systems. They still use a positive base, but have positive and negative digits, ideally the same number of positive and negative digits.

[@IznbranahlGoose]

When I first learned about it I really started enjoying playing with quaterimaginary which is 'base -2i' and lets you also fold the imaginary part of a complex number into a single 'base-4' series of numbers without negative signs or the awkward +(number)i part. When adding and subtracting you have the 'carries become borrows' flip flop and you have to skip over a digit since every other digit flip flops between real and imaginary. Remarkably multiplication works pretty much like regular multiplication except you have to deal with the oddities of 'carrying' and 'borrowing'. Division, on the other hand, is rather tricky but it has the one advantage of not having to compute a complex conjugate.

[@Hexa1296]

if you're worried about accidentally saying a slur, negative decimal also works

[@nereisian]

Given the unfortunate pronounciation of negadecimal, I propose two alternatives: antidecimal: literally the opposite of decimal debtimal: debts can be viewed as having negative money

[@WrathofMath]

I think antidecimal is good, though debtimal is pretty cute it only works well with decimal. Debternary isn't so smooth.

[@coopergates9680]

Don't (b-1)s' complement and bs' complement (for base b) have advantages over negative bases? I'd rather write -(229) as 770 than having to use 190 just to represent ten.

[@Roxor128]

This makes me think of 2's complement, used for representing negative numbers in computers. The top-most place has a negative value, but the rest are positive. For example, for 8-bit numbers, the top bit has a value of -128, and the rest are +64 down to +1.

[@TonyFisher-lo8hh]

Just stop being logical. Spoils a good fantasy story!

[@WrathofMath]

cool, don't think I've ever heard of that

[@n00bxl71]

Yes, but using the tens complement for negative numbers is far too logical. Negadecimal does not have this problem.

[@themightyripples6582]

I'm smoking weed and the "negadecimal" TTS was tripping me out but i did hear one time you forgot to switch the audio and said "decimal" rather than "negadecimal" - However you're presenting this very well and unless you weren't paying attention to what was happening you would know what you meant anyways... so rather than time stamping it I simply kept watching until hearing the TTS so much drove me to point this out. lmao! Great videos tho, I watch a lot of math creators here and you somehow stand out a lot of the time and also the videos have good quality!

[@erikrichards6944]

I too came here high wondering what the hell was up that. 😂

[@DougTheDouglyDragon]

I LOVE BASES ❤

[@StylishHobo]

BASED

[@MichaelPiz]

This video makes it to (negative) 10th base.

[@jan-pi-ala-suli]

go all in and use a complex base like -1+i

[@WrathofMath]

too many minuses for me

[@hazevthewolf178]

You've no way of knowing this upfront, but this video came along at just the right time. As one of my favourite fictional people would say, "Decidedly, I am unwell." This is a fun topic and I enjoyed your easy to follow exposition of it. When I go back to bed, in the spirit of one of Lewis Carroll's pillow problems, I'm going to bring a notepad and pencil with me and play with this concept. Cheers!

[@AstaryuuGaming]

Fun fact: -1 in base 10 is 19 in base -10, so in the example of 34 + 89 in base -10, you can also think of that -1 carry into the hundreds place as sticking -1 in negadecimal to the front.

[@sirnicholasiii]

every base is base 10

[@paperwhite3853]

Base 2 and base -i×sqrt(e^2) are shocked by this basephobic comment

[@Why553-k5b_1]

proof?

[@leeprice133]

​​​@@Why553-k5b_1the base number is always written as '10' in any positional numeral system using Arabic numerals. The word 'ten' and the numeral '10' only represent the same thing in decimal.

[@rubenvanderark4960]

​@@Why553-k5b_1in base 2, 2 is written as 10. Therefore in base 2, you can say "this is base 10". This works for any number because n^1=n, so every base will be represented by one copy of the base to the power of one (a 1 in what we call the "tens digit" in base ten) and zero copies of the base to the power of zero (a 0 in the ones digit), or 10

[@avovk1852]

which is base 1010 itself

[@AlreschaAndromeda]

Unless you modified the alternating sign for even terms only, so that negadecimal are symmetrical to the posidescimal I.e.: -1 (base 10) = 1 (base -10)

[@FaerieDragonZook]

Balanced Ternary is a fun and overpowered system.

[@WrathofMath]

Definitely got that one on my list, it's very cute and I didn't want to bring it up here because it's too fun to just mention and not dig into

[@thierrypauwels]

Balanced ternary is my favourite. Rounding a number is nothing else than cutting the excess decimals. You can start an addition of many numbers without knowing whether the result will be positive or negative. Ideal to represent quantities that have no natural zero point. In particular every scale that is logarithmic. A drawback is that one half has no finite representation, but two infinite sequences of digits: zero, decimal point, followed by infinitely many 1s, or one, decimal point, followed by infinitely many (-1)s.

[@FaerieDragonZook]

Some benefits of Balanced Ternary: Extremely good radix economy No - sign needed. Only 2/9 carries in addition table, even better than the 1/4 of binary. Negation is just flipping all the (+1) symbols to (-1) and vice versa.

[@gcewing]

So Canada has 10 provinces... or is that -10 provinces... I'm so confused.

[@MichaelPiz]

There's nothing positive about Canada, especially the temperatures.

[@thegrandminority8890]

"No matter what base we use..." Twos compliment be like

[@nanettepaschall3006]

why couldnt it be called inverdecimal

[@AlkalineOrSomething]

0:43 uncalled for

[@MathimaticalMathacy]

Real

[@shgysk8zer0]

What about signed bases? As-in signed binary representing {-1, 0, 1} and being notated by {0, 1, 2} (0-index). Or something like that.

[@tylerduncan5908]

This is called a balanced system. Balanced ternary is somewhat common in a couple fields dealing with electronics.

[@ricardojuliao84]

Ok,now you have to redefine all the Math

[@MGSchmahl]

Now do quaterimaginary

[@WrathofMath]

it's on my todo list; right after using a Clue board to do the integral calculus

[@2wr633]

should have wrote the carry as 19 :)

[@WrathofMath]

a good idea!

[@whtiequillBj]

why would you need subtraction or division with negadecimal? Isn't it redundant to the system its self? Also inversion is redundant.

[@Golden_Official100]

I love [[negadecimal]], and I understand why you'd use a TTS

[@wyattstevens8574]

My eyes: *see the thumbnail* My brain: * "Hello folks, and welcome back to Combo Claaa-" * (let me know if you caught that reference!)

[@WrathofMath]

his sets are very whimsical, I'd like to hang out with the guy

[@wyattstevens8574]

@@WrathofMath I thought about that because he talked negative bases once! And the "trail-off" (ellipses) was supposed to symbolize a crashing clock!

[@kornsuwin]

the intro is a strong start

[@WrathofMath]

let not the terrors reach you

[@davidnoll9581]

I was thinking about a similar thing with an imaginary base. I guess you would need 2 of them... and I guess the numbers couldn't quite be the same base... one would still be multiplied by i, so not that cool after all, just basically changing the base of the coefficients of the normal complex plane... but still interesting to think the complex plane as a pair of coordinates in a negadecimal coordinate system. Guess it would be sort of like splicing the top and bottom halves of the plane? Wonder what the riemann zeta funciton would look like represented that way..

[@matthijshebly]

Check out Balanced Ternary

[@xavariusquest4603]

I'm intrigued by 3 ÷ 10 being 1 remainder 7. Oh....and you cannot restore the original value because the introduction of subtraction allows a group of possible solutions but not ONE solution. This was silly

[@WrathofMath]

we call it a lark

[@rainerzufall42]

8:24 Wrong use of carry!!!

[@orangesite7625]

The thumbnail 😂😂😂

[@Cynderace]

bro says [[ Negadecimal ]] like he’s spamton g spamton

[@mauriceprosper9730]

I lost it with the TTS at 9:08

[@jaydentplays7485]

Oh am I a problem now? After all those unsolved equations? 9-15. 6-12. 44-121

[@torfley]

negawatt?

[@brenatevi]

I found the "negadecimal" voice in hilarious.

[@WrathofMath]

I ain't getting caught on any slips!

[@alicesproul8155]

how does one count in negadecimal?

[@WrathofMath]

1, 2, 3, 4, 5, 6, 7, 8, 9, 190, ...

[@ThePsyko420]

It seems to me -94 is more concise than 1906

[@TeagueChrystie]

yeah this is much simpler than "minus"

[@SixtyStone]

Ah yes using 2 bases and introducing confusion instead of writing one simple line

[@WrathofMath]

Way better!

[@proboiz_50]

There are 7251 views right now in _nega decimal_ base

[@SixtyStone]

Ah yes Canada invented negative numbers.

[@WrathofMath]

they're a wily bunch

[@SixtyStone]

@WrathofMath I'm ao glad they gave this away to us otherwise math would be uhh less uhm insert word here

[@oenwilson2486]

okay but why is every mention of "negadecimal" just the same audio copy pasted throughout the video and adds an unnecessary emphasis to its name... it bothers me a lot and it sounds more like he's *really* hammering on what the prefix of the number system is...

[@StylishHobo]

It's a joke

[@swirlingvortex09]

Wrath of Math HAS to do this. If he speaks "negadecimal" normally and there isn't enough spoken emphasis on the "e"... it would sound like a slur and be treated as a slur. It is way less socially messy for the Microsoft TTS or phonetic sound file to be there.

[@ernesto.iglesias]

I think he will left the giant elephant in the room for the end. How do you represent the positive 10, 1000, 0.1 or any 10^(2n+1)? 😅

[@WrathofMath]

Easy! For 10 in base -10, just think of it as adding 100 and taking away 90, so it is 190. For 1000 it's like adding 10000 and taking away 9000, so 19000.

[@shaggygoat]

10₁₀, 1000₁₀, 0.1₁₀ and 10^(2n+1) may be represented as 190, 19000, 1.9 and 10^(2n+2) + 9×10(2n+1), respectively.

[@naoromi9883]

Negadecimal can i borrow a fry

[@oneoftheHongKongers]

2:16

[@fredrik3685]

I don't want to sound negative but.....

[@elliotsyptyst]

a WHAT decimal

[@Yellow45678]

You a Retard

[@WrathofMath]

🤖

[@misterlau5246]

Aw, dude 😅🤓😈 I'll keep using linear algebra to represent negatives in an affine space of the positives 🤓🤣

[@sebas31415]

I can't say that I'm white

[@mistersir3020]

Lol we can't do math because of N.

[@epicstar86]

aight man

[@ammhg8642]

👍

[@WrathofMath]

don't be so negative

[@henrycook859]

​@@WrathofMathits a popular internet meme to put nega as a prefix before a unit. Be honest, did you intentionally clickbait the title?

[@WrathofMath]

not sure what you mean, I'm not genuinely done using minus signs and converting my whole life to 🤖N E G A D E C I M A L🤖 if that's your question

[@ammhg8642]

@@WrathofMath guess it was a misunderstanding I thought you were like VSauce, with a funny thumbnail and content Its just maths i didn't know

[@UK_parliament_English]

I like the system! But i think I’ll (sadly) have to stick to the “meddling” (-) symbol.

[@WrathofMath]

Unfortunately that meddling symbol does have its conveniences

[@GameJam230]

Tbh I’ve always thought the concept of inverse functions (subtraction) to be such an odd concept, as they almost always introduce the requirement for new types of numbers to exist. Allowing an inverse of addition allows the possibility that there may exist a number such that 5 + X = 2, which without negatives is not possible. Division as an inverse establishes the possibility that there exists a number such that 6 * X = 2, which isn’t possible without fractional numbers. It also allows some additional solutions to older equations, like being able to identify -2 and -7 as valid divisors (if even atypical) for the number 14 The creation of exponentiation actually establishes multiple new types of number depending on the context “inverse” is used in. One occurs by placing fractional values in the exponent, which is what we know as roots. These create two new types of number, through irrationals like the square root of 2, but also it establishes the need for a solution to the equation X^2 = -1, which establishes the imaginary numbers, or complex numbers which can also be added component-wise with “real” numbers. The other type of inverse to exponentiation occurs as the solution to equations like 18^X = 5, in which case we need logarithms. What I wonder is whether or not any other useful new types of numbers can be decided in this same way; by creating a function, defining its inverse, and then solving an equation that produces a result outside the domain of the original function. I mean, you can define new rules all you want, really, like saying there’s zero-divisors, or the Eisenstein integer system, or suggesting that there is a result when dividing by 0, and so on. New number systems can be made just fine, but what I’m more curious about is if our EXISTING number system can be expanded naturally this way, such as by defining an inverse to tetration.

[@blue_alan.becker__real]

9h ago

[@Xeroisawesome]

So however this video got recommended to me, I strongly regret it. You successfully managed to waste around fove minutes of my life. Perhaps the worst part of all this is your bizarre insistence on having some AI voice say "negadecimal" in a jarring tone shift each time. Have fun with your overcomplicated BS and irrational fear of the prefix "nega"

[@WrathofMath]

thanks I will!

[@atimholt]

I was hoping the solution would be to subtract the magnitude of the negative number from an infinite string of nines going off to the left.

[@WrathofMath]

a fun activity for another time, no doubt!

[@KingGisInDaHouse]

I dont like it. How do we know how far -7 is from -20 is geometrically from this.

[@AlreschaAndromeda]

Negadecimal is sucks! Because minus ten to the power of even number is always positive

[@WrathofMath]

What's wrong with -10 to even powers always being positive? I think it's charming!

[@itzmetanjim]

change the name to MEGAdecimal. unintuitive but MUCH MUCH cooler.

[@killianobrien2007]

TEN MILLION DIGITS!

[@TheObstalace]

N E G A D E C I M A L

[@WrathofMath]

🤖🤖🤖