วีดีโอ

@@dylangamerplayz4690 See: th-cam.com/play/PL2qvIMkhqXu0t6bZjo3PS9SZAoY0tcAxh.html&si=NL2Fc5tolBkZ5J8-

There are hardly any circumstances in which it makes sense to say that zero to the power zero equals one. See: th-cam.com/video/Ez1VWaG1ZGA/w-d-xo.htmlsi=0tuTNFzCCKndtZhM

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@@myachix I am curious - how did you segue from your channel’s content to a high school project involving division by zero? Here are some projects. 1) MIT Scratch is a software environment for children, which is always supposed to work, but it crashes on Not-a-Number (NaN). If it used transreal arithmetic instead, it would work. As the source code is in the public domain, Scratch could be corrected by implementing an emulator for transreal arithmetic. scratch.mit.edu 2) Floating-point arithmetic, used in computers, has an astronomical number of Not-a-Number values. If transreal arithmetic were used, the results would be twice as accurate. Try to think of all the cases where this would benefit the users of computer systems. 3) Many high school coding projects involve cases where Not-a-Number (NaN) could be produced as an error. One such is calculating the arithmetic mean of zero samples as 0/0 (NaN). If transreal arithmetic were used, this would be a correct answer of nullity, instead of an error of NaN. Thus transreal arithmetic could be implemented, in a high school project, to enable defensive programming. (I am not sure how much you know about programming but this will make sense to the programmers in your school.)

@@WandererOfTrades Just because something is undefined, it does NOT mean it cannot be done! th-cam.com/video/l-p2wwg8lSc/w-d-xo.htmlsi=Up69dHJXnLgppCTi

nah, dividing by zero is just infinity

@ What is zero divided by zero?

@nifegun well yes and no cuz it's infinity and negative infinity

@@transmathematica never said it couldn't be done Many have shown that it can be done and I never thought it couldn't be done for that dividing is just taking away until you have reached 0

@@Kristijan-n4d This video is not related to transmathematics. I have started a new playlist that discusses how to be a scientist. This interview is with an author who became a scientist late in life. She has published scientific themes for very young children. For the next three Saturdays, I will publish videos in this playlist while I make more videos on transmathematics. I aim to publish long form videos every Saturday. I will add shorts when I have them.

@@transmathematica Oh, yes! I didn't notice that😅 Sorry...

@@సత్యమేవ_జయతే Is this what you want? th-cam.com/video/N_TyOy2zFhM/w-d-xo.htmlsi=1aeS14gnjAde4QSr

Having the best cat in the West is pretty smart! Take it slowly and see how you get on.

@@timplayz-bf4sw Maybe I should have a prize for the shortest meaningful comment: ?

Nullity is not infinite but it is non-finite. I have scripted a video on this and have scheduled it for publication in about a month. We already know that the mathematics for black holes can be extended so that it works exactly at the singularity but no professional physicist has taken up the challenge - yet. dialnet.unirioja.es/descarga/articulo/6356671.pdf

@@brotheralaric7177 Try this one: th-cam.com/video/eQh0K5X9xVs/w-d-xo.htmlsi=fQnz20-5dfTe_NE3

It’s a joke - for native English speakers. It refers to a popular science fiction TV series called Star Trek. About 25% of my audience are not native English speakers so, maybe, I should not make jokes in titles.

@@transmathematica To be honest, I think that sometimes you SHOULD name your videos funny. I think that will increase the number of your subscribers😉

1/0 is an inverse of 0/1 but it is NOT a multiplicative inverse. An inverse is said to be “multiplicative” when a number multiplied by its inverse is equal to one. But transreal arithmetic has 0/1 x 1/0 = 0/0.

@@transmathematica OK, now I understand everything. Thanks!

And also, 1/0 is infinity, and 0^(-1) is epsilon. However, 1/0 = 0^(-1), so is infinity equal to epsilon?

@@Kristijan-n4d Epsilon is an empty symbol, it is a place holder, it can be replaced with something else. You have described the replacement that transreal arithmetic uses. Some people use different replacements. Epsilon can be replaced by very many things, so much so that Epsilon Totalisation is the most general method of totalising anything. It is the foundation of all totalisations: start with no symbols and build up from there!

@@transmathematica If epsilon can be replaced with something else, how is 0^(-1) = epsilon?

OK, I’ll bite. What do Wonder Woman and Superman have to do with division by zero?

​​@@transmathematicaWhy the denominator must be non-negative real number to make a transreal number?

@@Kristijan-n4dNotice that 0 = 0/1 = 0/(-1). Now the lexical reciprocal of 0 is both 1/0 and -1/0. If we want the signed infinities 1/0 and -1/0 to be different, so that calculus and physics work, then we must stop the ambiguity in the sign of the denominator of zero. An easy and convenient way to do this is to insist that the denominators of all transreal numbers are non-negative. Being non-negative is different from being positive because a non-negative denominator allows a zero denominator and this allows division by zero! If you read scientific papers on transmathematics you will see they often say “non-negative” not “positive.”

@@Kristijan-n4d First, you need to understand Polar Complex Numbers, <radius, angle>. Search for explanations on the web or in mathematics books or ask your school teachers. Second, you need to understand how the Riemann Sphere encodes the Complex Plane of Polar Complex Numbers. Third, you need to know Riemann’s mapping between his Sphere and the Complex Plane breaks down at the North Pole of the Sphere. Wolfram encodes this break down by the symbol 1/0. This is ONE symbol in itself, it is NOT one divided by zero, it cannot be used in arithmetic. It stands for all of the Complex Numbers that have an infinite radius, regardless of angle. This is called a “compactification of the complex plane.” Fourth, you need to understand how the Riemann Sphere encodes the Transcomplex Plane without breaking down. Points on an infinitesimal circle that asymptote to the North Pole map onto the Transcomplex Circle at Infinity. The North Pole maps onto the Point at Nullity. The Transcomplex Circle at Infinity and the Point at Nullity together provide all of the compactifications of the Complex Plane that are usually used in Complex Analysis. The Transcomplex Number 1/0 is the Transcomplex Infinity <1/0, 0> on the Transcomplex Circle at Infinity that lies at angle zero. All Transcomplex Numbers, including 1/0 = <1/0, 0> can be used in Transcomplex Arithmetic. Take a look at the following paper. Read whatever you can understand and think about the pictures. Good Luck! www.iaeng.org/publication/WCECS2014/WCECS2014_pp97-102.pdf

@@Kristijan-n4d Imagine someone has fired a nuclear missile at you. Would you like to intercept it? If your interceptor missile use floating-point arithmetic, you have thrown away half the accuracy, as against using transreal nullity instead of IEEE 754 NaN. That’s a good enough reason to divide by zero for me.

​@@transmathematicaCan you tell me a simpler example? No problem if you can't.

@@Kristijan-n4d If you write computer programs, having a positive and negative infinity is a lot easier than looking up extremal values in a library, though some computer languages already provide this. Nullity arises naturally as a defensive value or sentinel, for example when calculating arithmetical means in the corner case where no samples have been read. Here nullity is the sample value zero divided by zero occurrences. Of course one has to know transreal arithmetic to make use of this!

​​@@transmathematica I'm sorry, I'm only 10 years old. Can you tell me the simplest example of division by zero in real life?

@@Kristijan-n4d I didn’t expect young people to watch my channel. If you have learned all of transreal addition, subtraction, multiplication and division then you are the youngest person to do so. The previous record was held by an eleven year old. However, many six year olds have learned infinity - infinity = nullity as a way of avoiding a bug in Scratch. The simplest I can make this for you is to say that you must be able to divide by zero if you are to solve all of the problems that could arise in arithmetic. You will find that transreal arithmetic has prepared you to understand calculus - though it might be a few years yet before you study calculus.

@@Kristijan-n4d I haven’t done an example of that, but you can learn all of elementary transreal arithmetic here: th-cam.com/video/tdltT8-l9Nc/w-d-xo.htmlsi=yud7GuWJgsQBu7La

It is completely normal to say “log” for all bases, especially where the written form and the operations applied to it indicate the “natural logarithm.”

@@Kristijan-n4d By repeated applications of this sum: th-cam.com/video/zdKKQoI5hWE/w-d-xo.htmlsi=KzS8tLRocHvIHAJg

​@@transmathematicaThe link doesn't work. Can you just tell me, please?

@@Kristijan-n4d -infinity + infinity = -1/0 + 1/0 = (-1 + 1)/0 = 0/0 = nullity. Apply this repeatedly. Alternatively do a proof by induction after the first term is nullity.

@@transmathematica Ohh, yes! I compeletely forgot about it... Thanks!

Yes, 0 times negative infinity is nullity. Just write -1 instead of 1 in this proof: th-cam.com/video/n7OHK-VEMqk/w-d-xo.htmlsi=zISrg73WasgeoPff All of the basic operations of arithmetic are explained here: th-cam.com/video/tdltT8-l9Nc/w-d-xo.htmlsi=4vIYCoIeWPqLVM9Q

@@transmathematica Thanks! Oh, and also, I was watching your video "What is cosine of infinity?" and how is in that video -infinity + infinity and so on equal to nullity + nullity and so on?

There are a couple of things to note. First, there are different kinds of infinity. Many of them have the property that zero times an infinity IS zero. The easiest of these kinds of infinity occur in set theory. They are known as Transfinite Numbers. They can occur as Cardinal Numbers or Ordinal Numbers. If you want to find out about these infinities, look at set theory. Second, indeterminate forms deal with asymptotes, not exact numbers, such as exact zero or an exact infinity. I will make a video about indeterminate forms to explain how they relate to division by zero.

@@williamsprakties6523 No, but I did design a superset of real arithmetic and real calculus for which 1/0 is positive infinity and -1/0 is negative infinity. See from here: th-cam.com/video/JU86udWOgr0/w-d-xo.htmlsi=IFiC-QAjWU6HIWzx

I guess you are leaving breadcrumbs?

@@AsaWickham NUMBERS can have have an indefinitely long (never ending) decimal expansion of their fractional part but not of their integral part. For example, pi = 3.14159… , has a never ending fractional part, 0.14159… , but it has a finitely long integral part, 3. A LIMIT can have a never endingly long integral part, but then the LIMIT is not a real number, though the limit can be the transreal infinities discussed in the video, whence the video correctly states the arithmetic. Furthermore your proposal leads to the conclusion that infinity is unsigned, being neither positive nor negative, whence it is neither large nor small, though it does have a large magnitude. By your hypothesis, ∞ - ∞ = ∞; multiply both sides by -1 giving -1(∞ - ∞) = -1(∞); -∞ + ∞ = -∞; ∞ - ∞ = -∞; so ∞ - ∞ = ∞ = -∞. As your infinity has no sign, it cannot be used in calculus to compute, say, integrals from negative infinity to positive infinity (because there is no negative infinity and no positive infinity). Nor can your infinity be used in physics, whereas mine can and has been used to extend Newtons Laws of Motion so that they work at a singularity. See: dialnet.unirioja.es/descarga/articulo/6356671.pdf

Wow........ just wow......

How do you type the superscript zero and the division sign into a TH-cam comment? I can write pretty much any formula in LaTeX but I haven’t been hugely successful at copying and pasting into TH-cam. So how do you do it?!

I am curious to know why people transcribe part of a video into the comments. If you are a real person, you should know there is a full transcript in the video’s description. So, satisfy my curiosity, why do you do it?

@@transmathematica zero times infinity is nullity.