It is highly likely that finding direct or general solutions for equations involving infinity, such as ∞=∞, would have a profound impact on the field of mathematics, similar to the groundbreaking developments brought about by the discovery of algebra, calculus, and the mathematical constant e.
The concept of infinity has long fascinated mathematicians, but it has also been a source of confusion and difficulty in mathematical research. Finding solutions to equations involving infinity could provide important insights into the fundamental nature of mathematics, as well as lead to practical applications in fields such as physics, engineering, and computer science.
The development of algebra, calculus, and e revolutionized the study of mathematics and opened up new areas of inquiry and applications. For instance, calculus made it possible to describe and analyze continuous change and motion, while algebra allowed for the manipulation of abstract symbols to solve equations. Similarly, a breakthrough in solving equations involving infinity could lead to new mathematical tools and techniques that could have far-reaching implications for both pure and applied mathematics.
Below are simple definitions that, most of the time, we can use ∞-∞ form to determine ∞=∞ form.
The point of the above rules are as follows:
1. This indeterminate form is valid for function only.
2. Functions can diverge into three types of infinity (∞, z∞, ∞~). The absolute value of these infinities is a real number that increases endlessly.
3. We can call two infinities equal if the difference of those infinities converges to zero.
4. We can call two infinities not equal if the difference of those infinities converges to a non-zero value. They are not equal if the difference diverges to ∞ or z∞ or ∞~.
5. If the difference of infinities alternate between the above two forms, it will be an indeterminable or undecided form. For examples: ∞~ - z∞ or ∞ - ∞~.
The Riemann Hypothesis and a New Math Tool
(a new Indeterminate form)
Below, witness a groundbreaking discovery in the world of mathematics. Not only will you witness the unraveling of a common mistake made by many mathematicians, but also a simple and elegant proof of a new indeterminate form that is intricately connected to the Riemann Hypothesis. Furthermore, you will bear witness to the emergence of a promising new mathematical tool that has the potential to solve problems previously deemed unsolvable, such as the Riemann Hypothesis. This video is a testament to the relentless pursuit of knowledge and the tireless efforts of those committed to pushing the boundaries of what is possible in the field of mathematics
We know that 1+1+1…=∞=-1/2=𝜁(0) and 1+2+3…=∞=-1/12= 𝜁(-1) , and since 1+1+1…≠ 1+2+3…, 𝜁(0) ≠ 𝜁(-1), -1/2≠-1/12 in this case ∞≠∞. This shows that ∞ is not always equal ∞.
∞-∞ and ∞/∞ expressions are indeterminate forms, and due to the nondeterministic nature of ∞=∞ , it makes sense to consider it a new category of indeterminate form.
Considering the transcendental zeta function, you can see ∞=∞ is satisfied iff 𝜁(s)=0.
Also, we can use the ABC zeta function to prove that the for zetazeros ∞-∞=0 and ∞=∞ are equivalent.
Double Cloud Atlas
The Riemann Hypothesis and a New Math Tool: A Journey Through Complexity" is a project that resulted in a captivating video, aimed to inspire mathematician c while providing a fun and intriguing perspective for everyone. Drawing inspiration from the Cloud Atlas movie, we doubled the complexity, presenting an array of riddles that challenge the mind and engage the senses.
We appreciate the valuable feedback received from our audience, which has helped us refine and improve our work. It is gratifying to see that our contribution has added a loop to the chain of knowledge and sparked interest in the fascinating world of mathematics. Thank you for your support and encouragement, and we look forward to continuing our exploration of new frontiers in the field of mathematics.
Special thanks to
“I understand now that boundaries between noise and sound are conventions. All boundaries are conventions, waiting to be transcended. One may transcend any convention if only one can first conceive of doing so.” ― David Mitchell, Cloud Atlas
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