Science Forums 2

[CraigD]

Originally Posted by Don Blazys

if our variables are to represent non-negative integers, then:

(1) Which term has the better defined variables?

This doesn’t seem to me a meaningful question.

Per the given, all variables are non-negative integers. Because is undefined, and division by zero not permitted in ordinary arithmetic, the additional constraints and . These statements fully define the domain of the expression. It makes no sense to me to ask which terms has the better defined variables, as their definitions apply to them throughout the expression.

Perhaps Don means to consider the domains of 2 separate expressions,

(1)

and

(2)

The domain of expression 1 is unconstrained, other than the given (and unnecessary) requirement that they be non-negative integers. The domain of expression 2 is additionally constrained as above. However, it makes no sense to me to call a more constrained domain “better defined”. For a number to be better defined than another, the other must be in some sense less than fully, explicitly defined. All of the variables above are fully, explicitly defined.

To describe the domain of expression 2 as “perfectly defined”, and that of expression 1 as “abysmally defined”, as Don does in post #72 is informal and, IMHO, inflated and silly.

Originally Posted by Don Blazys

(2) Keeping in mind that unity is not an actual common factor but a "trivial" or "degenerate" common factor, which term is more suitable for representing actual common factors?

That 1 is a factor of every number is a key theorem of ordinary airthmatic. A formal system lacking such a theorem would little resemble arithmetic, and, in short, be weird.

Don appears to be misusing the terms “trivial” and “degenerate”.

Trivial is a relative term meaning, roughly, “not difficult”. It isn’t a formal term. Degeneracy is formal term (see the wikipedia link above), but isn’t applicable to a integer or real valued constant.

Originally Posted by Don Blazys

(3) Keeping in mind that what we do to one side of an identity, we must also do to the other, can we "cross out" the cancelled T's the way we were taught in school?

Although I’ve only a vague idea what Don means by “cross out … the way we were taught in school”, and am aware that many students are taught math very poorly, the following is true:



may be written

Originally Posted by Don Blazys

(4) What occurs at T=1 and what does it imply?

A division by zero occurs. In the usual axiomatic system of arithmetic of real numbers, division by zero is an error condition, implying that the expression has an indeterminate value, rather than one of the usual value of an expression that is an equation, true of false.

Originally Posted by Don Blazys

When answering these questions, please remember that the above equation is absolutely new to mathematics ( I discovered it only a decade ago) so there is, as of yet, no "general consensus" on what it actually means.

There are a infinite number of equations that have never been written. Most are of little interest.



makes for a good exercise in algebra to prove (see Algebraic proof of “Blazys equation”), but despite Don’s claims (eg: that it can be used to prove Fermat’s last theorem and Beal’s conjecture), appears to have no further utility, despite Don’s claims to the contrary, such as

Originally Posted by Don Blazys

It's proper interpretation is perhaps the greatest challenge that the mathematical community has ever faced!

and

Originally Posted by Don Blazys

By the way, there are also many very good professional mathematicians (including a well known N.A.S.A./ J.P.L scientist) that have endorsed my work and have indicated (both in writing and verbally) that it is both interesting and thought provoking. (I posted a few of their letters on my website (donblazys.com).

Also, claims such as these latter should be backed up with links or citation. Simply saying support for them is posted at website, and giving its homepage, is not adequate citation.

The past few post of this thread have largely been an exchange of accusations and denials between Don and Nootropic, such as

Originally Posted by Nootropic

One sign of crackpot mathematics is its implications and you fail to realize the implications your apparent discovery imposes.

Originally Posted by Don Blazys

Also, please back up your claims. If you think that my equation is "crackpot mathematics" then show us where the error lies.

Hypography’s site rules require that we back up our claims. However, Nootropic’s claim is, essentially, that Don’s claims are unsupported, and need to be backed up.

This post from another math forum thread reference to Scott Aaronson’s “Ten Signs a Claimed Mathematical Breakthrough is Wrong” Though Aaronson’s list focuses specifically on the NP complete problem, it’s applicable, I think, to math in general, and to this thread in particular. I think Don would benefit from considering how closely his own writing matches the signs in this list, and attempting to make it match less closely. Justly or unjustly, all experienced math readers apply similar heuristics in determining how much effort to put into attempting to understand a post, paper, or website. If your writing triggers a reader’s “BS detector”, it’s unlikely to be taken seriously by her or him, so ignoring such lists is unwise.

First on Aaronson’s list is

1. The authors don’t use TeX.

Hypography isn’t a publisher, so doesn’t have file contents format requirements such as requiring the use of TeX, but our equivalent of this sign is “the poster doesn’t use LaTeX”. Don, in 3 months of posing, you persist in writing mathematical expressions as difficult to read strings, rather than use hypography’s available rendering features. I’m uncertain why, but don’t like it.