The Most Important Equation Ever.

[Don Blazys]

To: Bignose.

 

My logic is not wrong.

 

Yours is!

 

When you say that "Pi" can be represented as the one symbol "1" in the base Pi system, you are hillariously wrong!

 

In the base "Pi" system, the value "Pi" is represented as the two symbols "10".

 

Besides, symbolizing "Pi" as "10" does not constitute an evaluation of "Pi".

 

Pi is transendental and therefore can't be evaluated in any base.

 

Pi can only be approximated.

 

Thus, to take any "approximate number" as a base is to render even the most simple numbers impossible to evaluate exactly.

 

For instance, how do you represent the value "7" in the base Pi system?

 

It takes an infinite number of symbols, doesn't it?

 

Thus, all such "wierd" number system bases are rather contrived, aren't they?

 

When I said that Pi requires an infinite number of symbols in order to be represented, I meant represented meaningfully.

 

"10" is not a meaningfull representation of "Pi", any more than "#" is a meaningfull representation of the expression: 5^(1/2)+7.

 

Thus, your argument that the expression: 5^(1/2)+7 can be "represented" using only the one symbol "#" is both trivial and meaningless!

 

Most of us would prefer to represent: 5^(1/2)+7 meaningfully as 9.23606...., even though it does require an infinite number of symbols.

 

Look at it this way. Every number that is not a non-negative integer requires an operation, (and therefore an extra symbol) in order to be properly, fully, and therefore meaningfully represented. Non-negative integers, on the other hand, are the only numbers that do not require "attached operations". Thus non-negative integers are the only "pure numbers", because they are not associated with any operation whatsoever. They are not "mixed" with symbols for operations.

 

The imaginary number: i=(-1)^(1/2) can indeed be trivially represented as "i", but it's meaningfull representation:

(-1)^(1/2) requires the two operations (and therefore the two symbols) "minus sign" and "radical".

 

The non-negative integer: 2, on the other hand, does not have any operation anywhere near it.

 

That's the difference between non-negative integers and all other numbers, and why I prefer to work with the former.

 

I already promised that I will, from now on, state up front the restrictions on the variables that I am using. Nobody likes confusion, so that's one dead horse you can now leave alone.

 

Don.

Edited October 29, 2008 by Don Blazys

[CaptainPanic]

The pi-based-system is uses "radians". It is totally functional, and widely used.

[Bignose]

Right, I made a small mistake there. But, nevertheless, irrational and transcendental bases do exist and are used.

 

The value of 7 in a base [math]\pi[/math] system would probably be an irrational number. It doesn't really matter if you think it is meaningful or not, it nevertheless can be done. And that's my point. We can choose any base so that any number can be written with just one digit.

 

Just the fact that it can be done defeats your logic that just a symbol x must represent a single digit (base 10) integer. Because any number, rational, irrational, positive or negative, can be represented by one character. It doesn't have to necessarily make sense to you or to anyone, it can be done.

[D H]

Now that we know the OPs true colors, is there any reason you have not moved this thread to its rightful home, Bignose?

[iNow]

I think it's still math. It's real actual math, too, not speculative. The OP had a point which has been proven wrong over an over. I've learned some new math knowledge from reading this thread, anyway.

[Don Blazys]

To: Bignose.

 

You don't understand the difference detween meaningfull and trivial.

 

Show me an example of a number other than a non-negative integer that does not require an "extra symbol built-in operation" and I will believe you!

 

By your "logic", I can represent not just any number, but the entire universe using only the one symbol @.

 

Utterly trivial.

 

Don.

 

To: D H

 

The great mathematician Karl Gauss once remarked that: "Mathematics is largely a point of view."

 

From my point of view, my "true colors", are "true mathematics".

 

My topics, are both quite entertaining and therefore quite popular!

 

I will soon be posting a straight forward formula that is even more astonishing than my "cohesive term":

 

(T/T)a^x=T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1))

 

which really is astonishing because it is the first and only elementary algebraic term in the history of mathematics that algebraically prevents us from "crossing out" the cancelled T's, and therefore engenders all kinds of interesting questions such as:

 

"Which term is more relevant with regards to the properties of non-negative integers?",

 

"Which term has the better defined variables?" and:

 

"Does the above true equation show that multiplication/division by unity automatically results in division by zero?" Like I said before, letting T=1 sure seems to suggest that, doesn't it?

 

From my humble point of view, these questions are truly profound and the only motivations for eliminating, moving or locking my topic would be fear and/or jealousy.

 

Don.

 

To: !Now.

 

Thank you. It is real math, and people really are learning and asking questions!

 

I'm new to posting in forums, and I'm not exactly sure what "OP" means, but from the context, I figure it means me.

 

Which point of mine was proven wrong over and over?

 

I'm really doing my best to bring only true (and therefore interesting) things to this forum so if I know where I made a mistake, then I will correct it immediately, I promise.

 

Don.

 

To: Captain Panic.

 

I agree that Pi based number systems are both functional and widely used.

 

They are also fun!

 

I sometimes use them in my own research.

 

Don.

[iNow]

You must have misunderstood me. I think you're wrong and also being rude to our resident experts, guys whom I've learned to respect and trust from their contributions. I'm just saying that I've learned math from reading the responses of DH and Bignose, not that what you are doing is correct math.

[Bignose]

Don,

 

this is getting beyond silly.

 

You are ascribing meaning to using Arabic numerals. A number is no more or less valid if it is written in a different way. By your logic, Roman numerals are less valid because they would take more than 1 symbol to write. II isn't good because it takes two symbols to write. But, 2 is okay because it takes one. Neverthemind that II and 2 represent the same thing. Those Roman numerals that only take one symbol to write must be really, special, eh? V, X, L, M, C, D. Those are the good ones, right?

 

It's a good thing that we don't commonly spell out the numbers. Because two is clearly inferior to 2. As is zwei, dos, deux, twee, due, etc. etc. All those require more than one character to write out.

 

It doesn't matter what you use to represent a number. So long as that number is clearly defined. I can write x = 2 = 1+1 = 3-1 = [math]{\sqrt{2}}^2[/math] = 14/7 = 1.99999999999 repeating = [math]-e^{i\pi} - i^2[/math] = II = zwei = [math]\int_0^2 y dy[/math] = any of an infinite other number of ways to result in 2. They all have the same value. Just naming something x and saying nothing else confers no meaning whatsoever on x.

 

And, yes, Don. Sometimes the entire universe is indeed represented by one symbol. When mathematicians deal with a very specific problem on a specified domain, a symbol that is often used to represent that domain is [math]\Omega[/math]. And, in regarding that problem, the is the entire universe to that problem. So, yes, the entire universe is often represented by a single character.

 

You will see this notation often when integrating over the entire domain. Something like [math]\int_{\Omega} \rho(\mathbf{r})d\mathbf{r}[/math] is common when integrating a density [math]\rho[/math] over a domain, for example.

 

=============

 

While I think that Don was very dishonest about his intentions and very self-aggrandizing at the beginning of this thread, there could be some value to the work. It may have implications about the Beal Conjecture. I do think that Don needs to start a new thread specifically about the Beal Conjecture and talk about his possible results there. He does seem to miss the point that just because a variable only takes 1 character to write out doesn't confer on it with any special meaning whatsoever. If you want to limit a variable to certain values, you state that as part of the description. Period.

[Don Blazys]

To:Bignose,

 

It might be a few days or so before I can post again as I have to go in for some tests and scans to determine the progress of my Alzheimers.

 

If this is my final post here, then thanks for remaining interested throughout.

 

Don.

[Don Blazys]

To: Bignose,

 

If I start a new thread on the BC, then can you post my proof in the very next post in LaTex so that other readers will find it easier to read? (I prefer versions #1 and #2) My website is perfectly safe to visit. It was created by the computer teachers at a Catholic high school.

 

Don.