Can this set be defined like this?
Good day
I'm currently researching my own extension of the real numbers, such as complex numbers, and I've come across something very interesting. I call the defined set (see image below) the shift set (it's related to the properties I've discovered). If it can and is allowed to be defined this way, I think I've found a really cool set. Perhaps there's something preventing me from defining this set this way?
Best regards and thanks!
(1 votes)
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So for the first time, it would be “The Shift amount”.
Moreover, this is not an extension of real numbers, because almost all body properties are no longer fulfilled here and in my opinion there is a logical error. You do not extend the real numbers, but only give the -1 another name. -1*(-1)=(-1)2. And then your definition of the addition no longer makes any sense, since then the distributivity laws of the real numbers would also have to apply. A body extension normally introduces properties that have not yet existed in the original amount. Neither do I see this really and at the same time destroy some important characteristics of real numbers that get the complex numbers.
How is the multiplication defined? That’s essential, I’m saying that you’ll find my useful instructions for (a+by)(c+dy). If so, I just don’t see her. I’m curious.
Edit:
What’s going on?
ay+ay=(a-a)y=0 -> ay = -ay (that is the meaning behind – in an addition)
So y=-y. Thus, y must be the 0 element of the addition.
So, for example, you don’t even have a ring, or you have y=0, and then you just have the real numbers.
So. No, I don’t think you have any meaningful definition. Especially because multiplication is not well-defined. What is 2*(ay)? It is
ay+ay=0? Then 2=0.
Thanks for the detailed explanation my intuition confirms. You may add that you can construct such a quantity of numbers naturally, only your purpose is unclear and above all the “cracking properties” that the user attaches to it I do not see.
You asked a question and the two people who answered you have taken your approach seriously and pointed out problems.
In return, you write infantile answers, and insult the responders who have taken time, especially for LoverOfPi, to deal with your proposal.
If you ask me, you should not only work on your mathematical work, but first of all on your attitude, your critique and your dealing with others.
You have asked if you can define the amount so and have received the well-founded answer that in this definition nothing meaningful (so nothing you could work on) comes out.
Let’s go Don’t discourage yourself, it’s in mathematics that a smart idea has usually come before someone else for a long time. What means that a previously unknown idea is usually not particularly clever.
What kind of rough qualities should the crowd have? She can’t be a body. Otherwise, I feel the crowd is not well defined, because unclear is what gamma should be exact now. But I’d like to be better informed.
Addendum for your supplement:
You don’t have to apologize for this, I was 16 and dreamt of discovering the world formula
This is a good attitude
No one knows everything, and I don’t know what a hyperrical ring body is. By the way, a body as a vector space has the dimension 1. But this is where your problems begin. Because the most famous scientists know one thing, they stand on the shoulders of giants:
https://en.wikipedia.org/wiki/Standing_on_the_shoulders_of_giants
Talk to you to deal with mathematics first you have to learn mathematics. You don’t have to know what’s a maximum ideal if you want to do analysis, and if you want to do numbers theory, don’t necessarily know what the Bairsche category set is. If you want to run stochastics, you don’t have to know the finite element method and if you don’t deepen the Malliavin calculus. But before you start to get into the mistakes and confusions of your own definitions, you should first develop the basics that are taught about substance in the lectures Analysis I-III, Lineare Algebra I and II, Numerics and Stochastics (the terms I named do not appear in any of the lectures :-)). Sensually you deepen one of the themes, with me was the analysis of functional analysis and function theory as well as numerics of ordinary differential equations and numerical calculations. I dropped algebra and stochastics.
Only when you are safe not only in the mathematical language, but also in the mathematical terms and know what a body is and in which it differs from a vector space and why a body considered as a vector space has the dimension 1 you can try to build on it and extend your feelers to your own particularities. A lot of success.