Without singularity numbers, we won’t be able to fully understand the universe or black holes. Singularity points are crucial in explaining extreme conditions where conventional math breaks down. Without them, much of the deeper aspects of math and physics would remain incomplete
It's hilarious, there is sarcasm but it is also the truth. "Bold step forward in maths" understanding the divide by zero error 😂😂👍 I say rewrite all infinity symbols with 1/0 in all equations.
?? there's a reason you can't just "let k = 1/0" the same way we did with i = √-1 1 = 0k = (0*0)k = 0*0k = 0*1 = 0 unless you reject 0*0 = 0, your invented "singularity numbers" are inconsistent
You're misunderstanding the concept of singularity numbers. When I define k = 1/0, it's not like regular math. 0k = 0 * 1/0 results in an indeterminate form 0/0, not zero. Similarly, 2k = 2/0 is undefined, not a regular number. You can't apply normal algebraic rules here because these are singularity points, not ordinary values.
what's the point of defining k to be the multiplicative inverse of 0, only for them to not actually multiply to 1? you say they multiply to "undefined", even though your whole point was to make a number system closed under division. you assert that a sum of singularity values is 0k, so it follows that 1k = (½+½)k = ½k + ½k = 0k the only way to reject the above statement would be to reject that multiplication distributes over addition. thus 1k = 0k, and likewise ck = 0k for any c ∈ ℝ. thus there exists only one singularity number, k itself, and k+k = k; all multiples of k are really just k. thus every number in this system can be described as either ℝ or ℝ+k, where operations with arguments in ℝ behave as in ℝ, and operations with any argument in ℝ+k will forever have +k. this is the exact behavior of undefined values
honestly i love your ingenuity and i think you would love to learn about ring algebras and their matrix representations. there are a lot of wacky number systems out there with weird properties but the one you set forth here just isn't internally consistent with, like, anything
i really appreciate the depth of your analysis! Just to clarify, Singularity Numbers aren’t intended to follow the same rules as real numbers. Think of them more like matrices, which don’t obey all the same properties as reals. For example, matrix multiplication isn’t commutative, yet matrices have their own consistent set of rules. If you’d like, could you compile all the properties and observations you’ve derived about Singularity Numbers? I’d love to explore your perspective further and even create a new video addressing these points in detail. Your insights are invaluable-thank you!
these aren't really like matrices because your number system doesn't obey the ring axioms. it seems like what you really need to do is DEFINE what properties your numbers DO satisfy. because you say very often "they don't follow the same rules". which arithmetic rules *do* they follow? i would recommend reading the wikipedia pages for Groups, Rings, and Semirings, so you can see what kinds of axioms you need to show are consistent in your number system. you need to pick an algebraic structure with some kind of multiplicative inverse in order for your axiom "k := 1/0" to exist - otherwise you're defining k in terms of an operation that doesn't exist. but there is no algebraic structure with any kind of inverse which your Singularity Numbers satisfy, usually because you can prove ck=k for all c∈ℝ (did you delete my other reply? lol)
You should look into Wheel algebras! I personally am not the biggest fan of these numbers though because in order for them to be consistent you have to reject distributivity of multiplication over addition among other things.
We can't simply ignore the concept of 1/0. Traditionally, we’ve tried to understand or solve it using 2D graphs or arithmetic, which is why it remains undefined in conventional mathematics. Consider this progression: 30/2 = 15 20/2 = 10 10/2 = 5 As the numerator increases while keeping the denominator constant, the results also increase. Following this reasoning: 3/0 > 2/0 > 1/0 > 0/0. Now, what if singularity numbers exist in a plane that is either parallel or perpendicular to the complex plane? This could open up a whole new perspective to approach these challenges. We’ll keep exploring these ideas and pushing the boundaries of what’s possible.
Lets do it right with redefine "e" to fractal. Dont let this no need of extra structures in mathematic for future. It will be better. Please contact me.
also why didn't you actually expand your power series 😭😭 the k terms don't just add to zero if you run with kⁿ=k for n≥1 then exp(k) = 1 + (e−1)k, sin(k) = sin(1)k, cos(k) = 1 + (cos(1)-1)k, and ln(1+k) = ln(2)k
This is what I thought too. I was about to upload the video, but then I realized something was wrong. Do you know what it is? We can't factor out k, because factoring implies the quotient is 1. But k/k is not 1-you can check this yourself. 1/0 ÷ 1/0 equals 0/0, not 1
I didn’t say it’s true for all x; I said x must be a singularity. Cos(k) = 0k = 0/0, and with k = 1/0, e^k = 0k, so they can be equal. About the Euler identity of complex numbers, if you multiply both sides by 2, it might look wrong, but it’s not-it just seems incorrect at first glance.
@@log_menus_1 If equality is no longer transitive under these singularity numbers what's the use of them? Is there anything interesting you can do with them?
@@applimu7992 of course you're absolutely right I completely misinterpreted what was in front of me. The claim is cos(k) = 1 + 0k this simply implies cos(k) = e^k which implies no contradiction. this raises a simple question: is this system consistent?
@@log_menus_1 well you know what, I spent a solid hour convincing myself that there are no actual problems with this number system. Sure multiplication is not distributive over addition, but it seems that at the very least, {0, 1, 0k and 1k} are all distinct elements of the space. from what you presented I see no problems. That's pretty cool. I can't tell exactly what kind of object it is. But it is definitely non-distributive, which makes it *almost* like a semiring, except that zero doesn't act like an annihilator (which effectively seems to completely decouple the numbers involving k and the numbers not involving k, for example, I can't uniquely define 0k*1k). I love abstract algebra!
YES this is what we need! I always thought that division by zero should be defined, just like imaginary numbers! 💥
Also, coupd this provide a better understanding for how gravity behaves at the center of a black hole?
Without singularity numbers, we won’t be able to fully understand the universe or black holes. Singularity points are crucial in explaining extreme conditions where conventional math breaks down. Without them, much of the deeper aspects of math and physics would remain incomplete
I love this idea! Personally, I’ve been using д^0=д,д^2=-д as an infinity, with 0*д=2/3. I think you would find it interesting to review?
What happened to the audio at the sections where you substitute in the series?
Mention timestamp!
@log_menus_1 there are 4 or 5 moments and it happened at every instance. Theyre quick to find in such a short video
It's hilarious, there is sarcasm but it is also the truth. "Bold step forward in maths" understanding the divide by zero error 😂😂👍
I say rewrite all infinity symbols with 1/0 in all equations.
wait for new numbers in future videos ...
?? there's a reason you can't just "let k = 1/0" the same way we did with i = √-1
1 = 0k = (0*0)k = 0*0k = 0*1 = 0
unless you reject 0*0 = 0, your invented "singularity numbers" are inconsistent
You're misunderstanding the concept of singularity numbers. When I define k = 1/0, it's not like regular math. 0k = 0 * 1/0 results in an indeterminate form 0/0, not zero. Similarly, 2k = 2/0 is undefined, not a regular number. You can't apply normal algebraic rules here because these are singularity points, not ordinary values.
what's the point of defining k to be the multiplicative inverse of 0, only for them to not actually multiply to 1? you say they multiply to "undefined", even though your whole point was to make a number system closed under division.
you assert that a sum of singularity values is 0k, so it follows that
1k = (½+½)k = ½k + ½k = 0k
the only way to reject the above statement would be to reject that multiplication distributes over addition.
thus 1k = 0k, and likewise ck = 0k for any c ∈ ℝ. thus there exists only one singularity number, k itself, and k+k = k; all multiples of k are really just k.
thus every number in this system can be described as either ℝ or ℝ+k, where operations with arguments in ℝ behave as in ℝ, and operations with any argument in ℝ+k will forever have +k. this is the exact behavior of undefined values
honestly i love your ingenuity and i think you would love to learn about ring algebras and their matrix representations. there are a lot of wacky number systems out there with weird properties but the one you set forth here just isn't internally consistent with, like, anything
i really appreciate the depth of your analysis! Just to clarify, Singularity Numbers aren’t intended to follow the same rules as real numbers. Think of them more like matrices, which don’t obey all the same properties as reals. For example, matrix multiplication isn’t commutative, yet matrices have their own consistent set of rules.
If you’d like, could you compile all the properties and observations you’ve derived about Singularity Numbers? I’d love to explore your perspective further and even create a new video addressing these points in detail. Your insights are invaluable-thank you!
these aren't really like matrices because your number system doesn't obey the ring axioms. it seems like what you really need to do is DEFINE what properties your numbers DO satisfy. because you say very often "they don't follow the same rules". which arithmetic rules *do* they follow?
i would recommend reading the wikipedia pages for Groups, Rings, and Semirings, so you can see what kinds of axioms you need to show are consistent in your number system. you need to pick an algebraic structure with some kind of multiplicative inverse in order for your axiom "k := 1/0" to exist - otherwise you're defining k in terms of an operation that doesn't exist. but there is no algebraic structure with any kind of inverse which your Singularity Numbers satisfy, usually because you can prove ck=k for all c∈ℝ (did you delete my other reply? lol)
You should look into Wheel algebras!
I personally am not the biggest fan of these numbers though because in order for them to be consistent you have to reject distributivity of multiplication over addition among other things.
We can't simply ignore the concept of 1/0. Traditionally, we’ve tried to understand or solve it using 2D graphs or arithmetic, which is why it remains undefined in conventional mathematics.
Consider this progression:
30/2 = 15
20/2 = 10
10/2 = 5
As the numerator increases while keeping the denominator constant, the results also increase. Following this reasoning:
3/0 > 2/0 > 1/0 > 0/0.
Now, what if singularity numbers exist in a plane that is either parallel or perpendicular to the complex plane? This could open up a whole new perspective to approach these challenges.
We’ll keep exploring these ideas and pushing the boundaries of what’s possible.
Is 0k=1?
because k=1/0
No...
0k = 0/0 which is not 1 ..
K = 1/0
Multiply by 0 on both sides
0k = (1/0)*0/1
0k = 0/0
So singularity numbers={...,-2k,-k, 0k,1k,2k,...}
Lets do it right with redefine "e" to fractal. Dont let this no need of extra structures in mathematic for future. It will be better. Please contact me.
You can contact me on my Facebook page, check out UA-cam bio
What's the reason for the not subscribing thing
I used reverse psychology...
when we restrict someone or tell them 'don’t do this,' it often triggers the opposite reaction.
dats cray cray!
Glad you find it interesting!
also why didn't you actually expand your power series 😭😭 the k terms don't just add to zero
if you run with kⁿ=k for n≥1 then exp(k) = 1 + (e−1)k, sin(k) = sin(1)k, cos(k) = 1 + (cos(1)-1)k, and ln(1+k) = ln(2)k
This is what I thought too. I was about to upload the video, but then I realized something was wrong. Do you know what it is? We can't factor out k, because factoring implies the quotient is 1. But k/k is not 1-you can check this yourself. 1/0 ÷ 1/0 equals 0/0, not 1
bro thinks his rené descartes
Je suis, donc je pense 😎
e^x = 1 + 0k
cos(x) = 1 + 0k
e^x = cos(x) is a contradiction.
So these numbers are not consistent? What gives?
I didn’t say it’s true for all x; I said x must be a singularity. Cos(k) = 0k = 0/0, and with k = 1/0, e^k = 0k, so they can be equal.
About the Euler identity of complex numbers, if you multiply both sides by 2, it might look wrong, but it’s not-it just seems incorrect at first glance.
@@log_menus_1 If equality is no longer transitive under these singularity numbers what's the use of them? Is there anything interesting you can do with them?
e^0 = 1 and cos(0) = 1, which is not a contradiction so this is faulty logic.
@@applimu7992 of course you're absolutely right I completely misinterpreted what was in front of me. The claim is cos(k) = 1 + 0k
this simply implies cos(k) = e^k which implies no contradiction.
this raises a simple question: is this system consistent?
@@log_menus_1 well you know what, I spent a solid hour convincing myself that there are no actual problems with this number system. Sure multiplication is not distributive over addition, but it seems that at the very least, {0, 1, 0k and 1k} are all distinct elements of the space. from what you presented I see no problems. That's pretty cool. I can't tell exactly what kind of object it is. But it is definitely non-distributive, which makes it *almost* like a semiring, except that zero doesn't act like an annihilator (which effectively seems to completely decouple the numbers involving k and the numbers not involving k, for example, I can't uniquely define 0k*1k).
I love abstract algebra!