How to Count in Base Negative 10

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Let me show you about negative numerical bases like Base -2 and Base -10, which have some surprising abilities! Leave a comment with which base you think humans should count in. Thanks for watching! Below are some links to other Combo Class sites that have been forming online:
Bonus Channel with more videos: / @domotro
Discord: / discord
Reddit: / comboclass
(And if anyone wants to help or support the channel in any way, the contact email I mentioned is on this channel's "about" page)
Here's a short video on my bonus channel where I show the answer of how to write 11.5 in Base -10: • How to Write 11.5 in B...
Some of the numerical base numbers that are mentioned in this video are Base 10, Base 10, Base 10, Base 10, Base 10, and Base 10... Just kidding, kinda. That IS how these bases would write their own base number haha (but we'll discuss that in a later episode). Of course it's easier to describe their names from a fixed standpoint like Base Ten, so let me rephrase it in more familiar terms: Some of the numerical base systems that are mentioned in this video are Base 10, Base 12, Base 6, Base 2, Base "1", Base -2, Base -10, Base -6, and a brief mention of some stranger potential bases at the end....
Disclaimer: Do not copy any actions you see in this video. This is for educational purposes.
Combo Class, taught by Domotro, is an unconventional learning experience where anybody (whether they're a fan of normal school or not) can become excited to learn rare things about math, science, language, and more. Also check out the shorter videos on the Combo Class Bonus channel. Thanks for coming to Combo Class!

Опубликовано:

12 ноя 2022

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Комментарии : 674

@ComboClass Год назад

Hey, since a lot of people requested that I make a Patreon, here is it (with various cool rewards for different tiers) www.patreon.com/comboclass

@Faroshkas Год назад

epic

@Anonymous-df8it Год назад

What do you think about signed senary? It allows you to represent both positive and negative numbers (like base -6), have simple addition and multiplication rules (like base 6) *_and_* reduce the size of the multiplication table by use of (+*+=+, +*-=-, -*-=+). Its digits are -3, -2, -1, 0, 1, 2 and 3

@HBMmaster Год назад

it's cool that seximal has gotten notable enough that videos like this mention it as one of the popular alternatives to decimal

@CuriousNeon Год назад

I found jan Misali in the wild, nice!

@Anonymous-df8it Год назад

Didn't expect you here!

@MXY... Год назад

holy shit jan misali

@gigaprofisi Год назад

Agreed! Seximal is my second-favorite base, thank you so much for making a video about bases!

@otakarbeinhauer Год назад

Can't wait to see where the imaginary bases or square root bases go. Fractional bases would be just flipped around the point and have the point shifted to the left of the 0th power.

@ComboClass Год назад

If it was based on a unit fraction (numerator 1) then it would be flipped like that, but what about Base 3/2?? haha

@shruggzdastr8-facedclown Год назад

@@ComboClass: ...or base-pi/e?

@anteeko Год назад

Dont forget Prime numbers base and Pi number base:))

@melody3741 Год назад

That last sentence made sense and also terrifies me

@Scigatt Год назад

Base phi pls.

@zecuse Год назад

14:03 Incidentally, this can be used to show that the set of natural numbers *N* (1, 2, 3, 4...) has the same cardinality as the set of integers *Z* (...-2, -1, 0, 1, 2...) and therefore are the same size of infinity as each other (aleph-zero, the smallest infinite set) which essentially makes them equivalent (|N| = |Z| because [obviously] |N|

@m6ty Год назад

This was exactly my thought on seeing this video!

@deleted-something Год назад

I thought exactly the same

@Magikarp_With_Dragonrage Год назад

≤ ≥ ≦ ≧ ≨ ≩ ⊂ ℕ ℵ here are some symbols you can use to simplify your comment with an edit!

@mulsenhfk Год назад

@@Magikarp_With_Dragonrage the heck are these symbols

@lox7182 3 месяца назад

you can just do (I'mma include 0 in N) f(x) = {x is even: x/2, x is odd: -(x+1)/2}. Well yeah this is pretty cool too I guess

@evancherpeski1876 Год назад

You should do a video on "in-between" dimensions that fractals reside in like a 2.36-dimension! Such great content!

@corsaircaruso471 Год назад

I second this!!!

@mohamedazadabdulrahman3226 Год назад

Do base 2+3i!

@onradioactivewaves Год назад

I find this suggestion to be highly irrational.

@GothAlice Год назад

@@onradioactivewaves F* Pythagoras! I LOVE BEING IRRATIONAL

@fuzzylogic33 Год назад

Ah, getting fuzzy

@tankfire20 Год назад

What I love about these videos is that it changes the way we think about concepts in math that we typically take for granted.

@michaelcherokee8906 Год назад

Like how, for example, most people dont realize that all numbers are representational, plus they assume counting in base ten is the only way to do it. Try explaining literally ANYTHING BUT base ten to the vast majority of people and theyll just ask why change from the norm, when in fact what defines norm is abstract.

@ten.seconds Год назад

@@michaelcherokee8906 And meanwhile the human brain is absolutely capable of doing all these weird maths without even noticing! Consider the following sentence: "I woke up at 9 am last Friday and after work I partied till 6 am on Saturday. Wow, I was awake for 21 hours!" I feel that a lot of people can do that in their head, and if you think about it, it is a kind of base-24 subtraction with two numbers that doesn't have a well defined 0 point with funny notations (am/pm).

@wrathofainz Год назад

@@michaelcherokee8906 "why change from the norm" is a valid question. As someone who fucks around with computers, seeing things represented in base16 can be rather irritating or jarring.

@michaelcherokee8906 Год назад

@@wrathofainz That isnt really relevant to my point. The norm couldve just as easily been any number of other bases, I think the only reason we naturally gravitated towards base ten is because that's how many fingers we have.

@seedmole Год назад

Base square root 2 sounds awesome, like basically an expanded binary that also includes a whole bunch of irrational numbers built from root 2.

@ethandavis7310 Год назад

You have to be careful with your definitions though. For example, what is the set of symbols you'll use in this base, and what do they represent? It's not entirely a given, as the entire base is centered around non-whole numbers, that the symbols should represent whole multiples of the base powers

@ComboClass Год назад

Wow the algorithm is liking this video more than usual! Thanks to everyone who's watching/commenting. After you watch this, if you enjoyed it, make sure to also check out my new episode about factorials: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-b2zhTrggRDE.html

@onradioactivewaves Год назад

Please keep this up, you have some amazingly interesting content!

@LaurieCheers Год назад

Really cool! The channel gives me the vibe of a Colbert Meanwhile intro - "but sometimes, folks, I like to throw on a stained labcoat, cut a whiteboard in half, and talk to the camera for 15 minutes in a backyard full of clocks for some reason, in my demented math class of a channel that I call... Combo Class."

@miggle2784 Год назад

Very informative as always. May the RU-vid algorithm bless you.

@GeoffCanyon Год назад

A long time ago I was in a high school math competition where they gave a lecture on a topic (that was supposed to be new to everyone) and then gave us a test to see whether we could apply what we had learned. The subject was base -3.

@guyedwards22 Год назад

Something I really enjoy about this is that it makes the fact that the cardinalities of the naturals and the integers are the same somewhat intuitive. If you listed the binary digits in order, there is a one-to-one correspondence between the integers encountered in base 2 (the Naturals) and the integers encountered in base -2 (all integers)

@coopergates9680 Год назад

That match isn't confusing. What's more counterintuitive is that there's the same number of naturals as there is rational numbers.

@aradziv89 Год назад

My favorite counting system is called phinary - as one would guess, it's based on the number phi (ie. the golden ratio). Being less than 2, it still requires 2 digits but there's a lot of redundancy as numbers can be written in a lot of different ways. This writing system does actually allow to write every natural number, as well as some irrational ones!

@ComboClass Год назад

Yeah I love that base, it will definitely show up in the “irrational bases” sequel to this video coming before long

@burkhardstackelberg1203 Год назад

I love base -1+i - no way to count all Gauss (complex) integers with less symbols, but it goes crazy!

@Anonymous-df8it Год назад

???

@dekox Год назад

This was so awesome! I kept smiling and laughing through it. Really brought me back the sense if wonder I would feel when watching the old school numberphile videos. I actually can't believe that (to my knowledge) none of the math/science channels has covered this topic yet. Can't wait to see the next ones.

@CleverJester95 Год назад

Absolutely loved this, I was impressed with the performance and then you dropped "wagstaff" and really got going and your math was super impressive and well explained. Thanks for making this.

@thomaskn1012 Год назад

I thought tau vs pi was paradigm shifting and ground breaking but this non-traditional base counting is also quite intriguing.

@kindlin Год назад

I was waiting to see base-pi. Ten (10) would be 3.01212011.... (3*pi^1 + 1*pi^-2 + 2*pi^-3 + ...). All numbers that are NOT pi, will be a transcendental. Only the number pi, or a multiple of itself, will be an integer.

@kindlin Год назад

I found a general way to solve for any value with any positive base, but it doesn't work well for negative bases. The back and forth nature of the places makes it harder to find a general formula.

@studyhelp7479 Год назад

Very clever -- very clear -- great fun! And VERY WELL DONE! Love the way you deliver very technical material in such a great way. Please deffo carry on doing what you are doing. THANKS! CHEERS from the UK! ;-)

@santiagovillarroel5023 Год назад

So glad youtube recommend me the Levels Beyond Exponents video. I have since watched every video and I'm eagerly awaiting the next. Great stuff!

@JonathonV Год назад

What a neat idea! Thank you for piquing my curiosity! I will have to look into that more!

@johnsmoak8237 Год назад

This is on my list of comprehensive teaching materials to use for lesson planning. It's so refreshing to meet people who feel joy so pure for such seemingly trivial work as mathematics can be. I hope I inspire students the way you always inspire me to keep solving

@mrTii Год назад

Your enthusiasm is amazing!

@kikivoorburg Год назад

I’d been thinking about base 2i recently, and the confirmation it does work has inspired me to go mess around and see what I can figure out! Thanks!

@HipNerd Год назад

One of my new favorite math channels. This channel is like, 'what if Grant Sanderson worked out of a junkyard'. Which, I mean as a joking, but sincere, compliment.

@rilakkumabeth Год назад

I only found your channel yesterday and I’ve watched so many of your videos and love them even though I’m clueless with complex math but enjoy learning. But some basic maths videos would be great 😂

@octoberdx Год назад

I've recently educated myself in negative bases and started to get some concepts of them (Through Wikipedia I may admit), and I'm glad to find someone else who has a genuine interest in these kinds of things. This totally helped my understanding somewhat, so thanks!

@elliwesishawkins4799 Год назад

This is the first video of yours I’ve seen and this is chaos I’ve been waiting for

@demoguy08 Год назад

Fascinating, such a simple yet mind-bending concept.

@NoOffenseAnimation Год назад

I always look forward to these videos

@neonsilver1936 Год назад

Alright...I'mma be straight up real with you dude. Your channel has me thinking critically about math, and I like it. I dare say that may be a "mission accomplished" for at least one viewer lol

@oitthegroit1297 Год назад

The fact that it is possible to contruct a numerical bass using positive integers, negative integers, fractions, real numbers, imaginary numbers, etc. has me thinking: What about complex bases, split-complex bases, dual number bases, quaternion bases, and other such bases based on strange types of numbers? What about combinations of those bases? And, most interestingly, what if variables and equations were somehow incorporated into the numerical bases themselves? My mind is blown by this video.

@OmegaFalcon Год назад

This is the best math course, I'm fucking excited for base imaginary numbers

@quinn9334 Год назад

this whole video is so delightful, haha. The outfit, props, background... the constant dutch angle adds a lot too ^_^

@memesifoundonline Год назад

I love this topic, and I don’t know why. Great video!

@dranorter Год назад

I think the appeal comes partially from the plausibility that some society could've decided to use these counting methods.

@karlwaugh30 Год назад

Awesome video. Fascinating in its ridiculousness and something I hadn't come across before. Also, I wanted to point out, if you start graphing the relationship between the "lexicographic" ordering of the digits (1,10,11,100,101...) against their "value" (1, -2, -1, 4, 5...) etc you get something with a certain amount of fractal self similarity when zoomed out.... Which is fun

@imcwaszec937 Год назад

Yes. See beta expansions, Pisot numbers, discrete dynamical systems and Rauzy fractals (dragons in general). ⏲

@EggZu_ Год назад

I love this format and the personality :D

@cubicklecub Год назад

Loved this one! Hope to see the complex part soon!

@gali01992 Год назад

This is so crazy! And the worst (best?) part about it is it actually makes sense! Great video!

@justRD1 Год назад

Bro! Instant subscription! How freaking fascinating!!

@derfunkhaus Год назад

This is great. You are an excellent teacher. Looking forward to more weird bases.

@the_jono Год назад

I literally started looking at base 2i before you even brought it up... it's great! I think you may need 4 symbols, though...

@waddupbro Год назад

Great video as always! Can't wait to see someone recommend we use negative bases

@christosmani Год назад

Yo dude, cant wait for the rest!!!! Love how it's so easy to make sense!!!!

@WontTrout Год назад

What an excellent video! Man you come up with some whacky stuff. 👍👍

@ericgolightly8450 Год назад

*w h a t* That's pretty cool You can have a bijective base 1 though

@ComboClass Год назад

Yeah that's like tally marks, but bijective bases are different than the standard positional rules I listed here, and bijective base 1 isn't always even considered "positional" as the position of the digit doesn't affect its value

@dasten123 Год назад

Woah dude! This is super cool! I would have never thought of that. Awesome stuff! :D

@docopoper Год назад

I wonder if you can represent all the complex numbers using an imaginary base like base 2i.

@docopoper Год назад

Oh x3

@ericgolightly8450 Год назад

You might be able to do that.

@Anonymous-df8it Год назад

You can!

@tsjbb Год назад

What an awesome video, thanks!

@BrianTonerAndFriends Год назад

I do a lot of work with a lot of numbers in different bases, and I just want to say I appreciate all the clocks. They remind me of how all the numbers tick at different speeds and are absolutely maddening. I don't know if that is the vibe you're going for there. But considering the topic, I thought it fit

@RibusPQR Год назад

This is a really clear explanation. I love it.

@alpheusmadsen8485 Год назад

I really appreciated the video! I have experimented with different bases (including balanced ternary, base 100, and base 2i), so I enjoyed seeing this, too. I personally don't consider my understanding of a base to be "complete" unless I've done addition, multiplication, and long division in the base. I have also experimented with "variable" bases -- both bases that increase by one, and bases using the dice of Dungeons and Dragons -- and they have fascinating properties of their own!

@jppagetoo Год назад

I have always found the different counting bases to be very interesting. We are so focused on base 10 (and to some degree base 2) that we forget what each digit really means. It have not been lost me on me that prime numbers and the bases we use for counting have a relationship. I just found your channel, this is right up my alley, I'll give you a sub and explore some of your ealier content!

@bdubbsmark Год назад

This just broke me. Craziest thing I've seen on this platform in a minute!

@pacefactor Год назад

Im sold. there is actual usefulness in having all negative numbers being represented with even digits and all positive numbers represented in odd digits.

@ianm1462 Год назад

New to this channel and I’m not a math guy but this was excellent. This has both Bill Nye and ‘guy shouting in the park’ vibes and the end result is a 15 min math lecture that held my attention throughout. Subbed!

@NFSHeld Год назад

I have never watched any video of yours. Came to this video with the expectation of an interesting theoretical approach, the intro and setup made me expect a goofy, silly video with purposely bad logic, but now, I have watched until 3:22 and I have to say even though it constantly makes me expect this video is going to turn comedy skit in the next sentence, so far, it is the best video on number bases (regarding pace of speech, representation, unambiguous choice of words, train of thought continuity, etc.) that I've seen in a very long time. Unfortunately, I don't have time to finish watching, but I wanted to let you know about this astounding impression your work has made "on first chance". Keep it up!

@solveforx314 Год назад

One thing I'm noticing with these negative bases is that places corresponding to odd powers count backwards, while the even-numbered places count forwards. For example, the negative decimal number following 198 (or 18 in regular decimal) would be 199, but then after that would be 180. If you think about it, this actually makes a lot of sense, since to add a ten, you have to subtract a negative ten. This might also be helpful knowledge to anyone attempting the bonus challenge :)

@dylanh333 Год назад

You have no idea how long I've pondered fractional bases... Subscribed!

@2001pulsar Год назад

That almost hurt my brain. Very thought-provoking. Thanks

@tenix6698 Год назад

Awesome editing and presentation!

@ryansullivan3085 Год назад

Ok this is significantly cooler than I was expecting lol

@MakerOfTheSillyShow Год назад

I feel like the representation of negative numbers is a really cool way to demonstrate the idea of countable infinities!

@dukefleed9525 Год назад

I love your videos!

@averysnyder4794 Год назад

this was amazing! mind blown

@minecafe Год назад

That is absurdly cumbersome and at a glance it has no purpose. I love it! Can't wait for 2i! 😁

@joaopaulocoelho5401 Год назад

FANTASTIC... just love it!! now, the rules for the four fundamental operations :D

@s4ad0wpi Год назад

I find that throwing Pi into these types of questions makes for some great patterns numerically... What does counting in base Pi look like? I'd love to see it!

@ComboClass Год назад

I’ll be including base pi in a future video along with the even more functional base root-2 and base golden ratio

@SkylarStJohn-mo4yi Год назад

@@ComboClass golden ratio!! yes

@seijirou302 Год назад

@@ComboClass subbing so i don't miss the base pi video. I've always wondered what that would look like.

@themonkeyman2547 Год назад

Are radians a base pi counting system?

@mattt.4395 Год назад

now do base -3

@cybermanne Год назад

Very well explained!

@NotSomeJustinWithoutAMoustache Год назад

How do you have less than 100k subs? This is genuinely one of the most interesting Math channels out there.

@sylvannight6153 Год назад

o.O Fun vid as always!

@Fortuna272 Год назад

Love how I'm being held hostage at someone's backyard and an unhinged TA is trying to get me to pass the course I'm struggling with.

@parkerbelholland1037 6 месяцев назад

Great explanation

@owlsmath Год назад

cool video! Never saw this before with a negative base. 👍

@dannydewario1550 Год назад

For those who were curious, writing 11.5 in base (-2) is 11100.1 and in base (-10) is 192.5 Edit: I got more curious and wanted to know what other fractions looked like in base (-2) *digits in brackets signify them repeating 1/2 = 1.1 1/3 = 0.[01] *and* 1.[10] 1/4 = 0.01 1/5 = 0.[0111] 1/6 = 0.0[1] 1/7 = 0.[011001] 1/8 = 0.011 1/9 = 0.[011] 1/10 = 0.01[1011] .....and that's as far as I've gotten, but it's interesting that 1/3 can be represented two different ways in base (-2). There could be more examples of this, but I'm not completely sure. Maybe this is the only occurrence in this base? I wondered if adding these two different representations of 1/3 would result in 2/3. And sure enough, if we add 0.[01] and 1.[10] together, we get 1.[1], which is correctly 2/3 in base (-2). I'm not sure how you actually do 0.[01] + 0.[01] to get 1.[1] because "carrying" seems to fall apart in base (-2). But it looks like when you don't have to carry any digits things will work out just fine.

@anshbarhate2791 Год назад

Wouldn't 11.5 in base -10 be 191.5?

@dannydewario1550 Год назад

@@anshbarhate2791 Close, but if we break apart 191.5 into it's components, we'll see it adds to 10.5: 191.5 = (1 x 100) + (9 x -10) + (1 x 1) + (5 x -1/10) Putting it all together: 191.5 = 100 - 90 + 1 - 5/10 = 10.5

@Humulator Год назад

the 1/3 thing happens in base 10 too, 0.9999999... is equal to 1.

@oitthegroit1297 Год назад

Cool, now write pi and e in base -10 :-P

@love2o9 Год назад

When they don't talk about bijective bases 😔

@ComboClass Год назад

Don't worry, there will be lots more bases mentioned in future episodes. This was just about standard positional ones following the common rules I listed

@KubGov Год назад

Looking forward to the videos of fractional bases and radical bases

@dranorter Год назад

Phigits (base phi) and figits (Fibbonacci "base").

@coltenh581 Год назад

I love everything about this

@TalenLee Год назад

I have no idea why I'm here but I am here for this strange person hollering in the backyard about numbers while things burn

@UberHummus Год назад

shockingly awesome stuff.

@lugyd1xdone195 Год назад

This is somewhat reminescing of Roman numbers where they basically count in numbers -5 up to 5 depending on its position to higher numbers. Its interesting how similar yet different they are.

@irukard Год назад

This is effing awesome :)

@laskey2175 Год назад

Using negative base counting we can label all negatives with positive integers. That's amazing. Love the video!

@ethandavis7310 Год назад

To touch on the point of not needing a negative sign, the amount of data needed to represent any given positive number in a negative base system as you describe here is greater than the amount of data required for a positive number representation in a positive base. If you're working equally with positive and negative numbers, then this gets ammortized out to be the same as a natural base, but if you're only working with positive integers you're still wasting data. Similarly if you're working with exclusively negative numbers you could just use a positive base and neglect the negative symbol and still use less data. Also: I appreciate the time you took to not gloss over the conventional rules put in place to define the number and ordering of symbols used in the natural base definition, and how you acknowledged that they needed to be bent in order to get a negative base to work. These are very often neglected when talking about irrational or complex bases. I hope you take the time in your next video as well to acknowledge that symbols pretty much lose all meaning in the context of an irrational base unless you rigorously define them

@ikemeitz5287 Год назад

Ok, I paused at your question of "what's 11.5 in base -10?" In regular base 10, the position after the decimal point is filled in by: 10^-1 This means that in base negative 10, the position after the decimal is: -10^-1 So, before we try to get 11.5, let's just get .5. Any digit after the decimal is going to subtract from the total. So, to get .5, we need to start with a number that's higher. 1 in base -10 is the same as 1 in base 10. 1 minus .5 is .5. So, 1.5 in base -10 is .5 in base 10. Alright, we're halfway there. To get 11 in base -10, we need to jump all the way to the third position (-10^3), which gives us 100 (which is 100 in base 10). Now, this is too big, so we need to take away some. The second position (-10^2) allows us to do that. Let's do 190 (which is 10 in base 10). To add just one more, we only need to add a digit in the first position (-10^1). This allows us to reach 191 (which is 11 in base 10). Almost there. To get 11.5, we need to remember what we did in the beginning. The first position after the decimal subtracts, so let's go up to 192, then add our subtracting first position after the decimal (-10^-1): 192.5 We did it! 192.5 in base -10 is 11.5 in base 10. We can even use this method to calculate tricker numbers. If we wanted to represent 11.75 in base -10, we need to go up to 192 (12 in base 10), come down to 192.3 (11.7 in base 10), then come up to 192.35 (11.75 in base 10).

@UnlimitedRadioButNoSoap Год назад

decent vsauce2 impression🧐

@4ffff2ee Год назад

that gives me such a strong roman numerals vibes (like how you would put "I" before "V" to make a 4, it's basically -1 plus 5)

@pvanukoff Год назад

Awesome stuff! Surprised Numberphile hasn't done something on this yet.

@kylben Год назад

Those neighbors in the house right on the other side of your fence must love this.

@Swag22ify Год назад

I loved the enthusiasm.

@dirkroosendaal2254 Год назад

I love how crazy you are about this, or just math in general I suppose. I myself LOVE math but as we all may know, people tend to think its a bit borrow. Thats why I love seeing how crazy you are about it, i think i need to watch more of your videos

@snoowbrigade Год назад

I love combo class!

@Ralyx0 Год назад

This was awesome.

@friedrichmarkus3574 Год назад

How does subtraction and addition work with negative bases?

@danieljmarvin Год назад

So, base 1 is different because it is a base that does not rely on the same level of symbolism. In higher bases, you have the b-1 symbols to memorize and then you build. In base 1, you use pure space to map to the number. Because of this, you do not need a 0 or a place holder symbol. For example, the dots you used were in base 1. I like to refer to this as different tiers of symbolism. The base 1 is a tier 1 symbolism, normal bases are a tier 2 symbolism. It's fun to think about.

@chri-k Год назад

unary is not a valid base because it can’t represent a fraction. it’s a valid number system ( you could do the following: .1 = 1/2, .11 = 1/3, .111 = 2/3, .1111 = 1/4, .11111 = 3/4, &c. ), but then it is no longer a number base and it turns all irrationals into .1 repeating,

@danieljmarvin Год назад

@@chri-k I hear what you are saying but you are assuming that unary uses a higher level of symbolism that it actually is. It's formal in that sense. To have a fraction you need to explicitly write the fraction out. So 4/5 would be (°°°°/°°°°°). That's why I called it a lower level of symbolism. Tangentially, with lower level logic you also have things like this with number like successors. So 0 is 0. 1 is S0 and so forth. But, within the system you are NOT allowed to say "and so forth." That's what makes it formal. For example, if I wanted to say 10 I could NOT say 0 with 10 S's before it. I would have to say SSSSSSSSSS0. Otherwise it defeats the whole point of being formal. "And so forth" is an observation ABOUT the system. You have to make another system that allows for rules about the system to be in the system. (This is a system that allows for induction.) My point is that there are different levels of symbolism one can use and they are ordered. I'm just pointing out a level that comes before what we normally think of a counting system.

@grakuynosc7270 Год назад

@@chri-k It is because decimal fractions cant work in the unary system because 1 to the different powers still equals 1. Just use normal fractions. 1/2 in the unary = 1/11

@Anonymous-df8it Год назад

The general case for this is bijective number bases. The digits go from 1 to b rather than from 0 to b-1. The others do have unwritable fractions, but at least some can be written down (e.g., bijective decimal 8/7=1.142857142857..., just like in regular decimal)

@the_yuty Год назад

You sound a lot like Kevin from Vsauce 2 lol. This is really trippy, and the number stuff is cool too!

@TheHamahakki Год назад

You just blow my mind.

@samuelthecamel Год назад

Hey, you should take a look at p-adic numbers! It's a somewhat related idea where you take our standard numerical notation, change the rules a bit (in this case, allowing for infinitely long numbers *before* the decimal point), and now you're able to represent numbers you'd need an extra symbol for before (rational numbers without the decimal point, irrational numbers without the decimal point, negative numbers, and even imaginary/complex numbers!)