Science Forums 2

[Don Blazys]

To:Craig D.

When discussing the domains of the variables in the equation, I did say that the terms should be considered or taken seperately. However, we are not discussing the definitions of numbers, but of variables.

In other words, we are discussing the fact that any variable is defined by it's domain, and if two different variables have the same domain, then they have, in essence, the same definition.

The concept is very simple. If we define the variables a and x as:

a={0,1,2...} and x={0,1,2...},

then a and x mean the exact same thing. However if we define a and x as:

a={1,2,3...} and x={0,1,2...},

then clearly, a and x mean two different things!

To put it in yet another way, if we let the symbols:

"a" or "{1,2,3...}" represent the word "cat", and

"x" or "{0,1,2...}" represent the word "dog",

then without "Blazys terms", we would forever be forced to conclude that cats are dogs because all we would ever have is:

a={0,1,2...} and x={0,1,2...}.

So you see, by the proper restriction of domains, "Blazys terms" provide us with a great improvement in definition!

That's a good thing, because only an idiot would call a cat a dog!

I am making no claims whatsoever, but simply allowing the equations:

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

and (it's factored form):

((T/T)a^(x/2))^2=(T(a/T)^(((x/2)ln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)))^2

to speak for themselves. They, not I say that letting T=1 is not possible. In other words, they, not I say that common factors, when they are allowed to become "trivial", clearly result in division by zero!

How would you "cross out" the T's in the above equations?
(By "crossing out", I mean "cancelling out" so that the cancelled T's "disappear".)

Common factors are not unity, period! In fact, the phrase "a common factor of unity" is actually a "misnomer" in that it is supposed to "mean" that no common factor exists! Therefore, eliminating the possibility of multiplication by unity is not "wierd" but a basic concept of number theory! I'm simply the first to write an algebraic term that reflects that concept perfectly.

You see, in number theory, unity is never viewed as a "multiplier" but as a "multiplicand". The reason for this is that the fundamental theorem of arithmetic tells us that every factorization is unique. Thus, if we allow multiplication by unity, then the number 6=1*2*3 would also be "factorable" as 1*1*2*3, 1*1*1*2*3 and so on. The sums of those factors would then be 6, 7, 8 and so on, and concepts such as "perfect numbers", "abundant numbers" and so on, would all collapse!

"Blazys terms" were designed for use in number theory. They are the first and only algebraic terms that don't allow trivial common factors to creep in to our equations. Moreover, they prevent the loss of cancelled common factors, allow us to develop incredible one and two term prime counting functions and present us with an entirely new and more rigorous form of calculus. To say that there are an infinite number of ways to write an elementary expression such as a "Blazys term" is simply ludicrous. There is, essentially, only one way to write a "Blazys term" (where T>1). All the rest are simply "variations".

None of the letters on my website are forgeries! Sorry, but I only began using a computer recently, so I don't know how to set up "links", nor do I know how to write in "LaTex" or put up "Smilies".

Euler, Fermat and Gauss didn't use LaTex either.

It doesn't make me wrong, just "old fashioned".

Don.