Hi everyone,

Assuming that the Kakeya conjecture is as stated on this website and I haven't mis-understood any definitions...

https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2013-03/finite_field_kakeya.pdf

....the Kakeya conjecture is quite easy to prove to be true. Actually, the proposition holds even if the Kakeya set is allowed to be such that it is non-compact, instead of compact as the actual conjecture requires.

I don't have much of an understanding of measure theory, but according to the definitions of Hausdorff dimension and Hausdorff measure, it is easy to show that the conjecture holds. If there is an allowance made for non-integer dimensions--e.g., d = 1.5--then in that case, the conjecture is certainly false...the dimension can be proved to be one less than what is stated in the conjecture if non-integer dimensions are allowed (I have a good way to define non-integer dimensions).

I wonder what is going on? Is it the case that, as with my almost exclusive understanding of relativziation in theoretical computer science (at least at first), I have somehow acquired in modern times the best understanding of real analysis, topology, number theory, abstract algebra, set theory, and basic logic of every math person who has ever lived so far? If so, then I am certainly happy about internet websites like Wikipedia and my ability to acquire textbooks.

The proof isn't extremely valuable or sensitive; maybe I would share it, it wouldn't impact any of my more secretive ideas that I've thought of.

Perhaps I misunderstood a definition or two in the conjecture; it does happen, I'm prepared to be challenged regarding the truth of the Kakeya conjecture as stated if the dimension is restricted to be an integer, or of the conjecture, "K (subset of R^n) has Hausdorff dimension (n-1)", which is true if the dimension can be real-valued.

I haven't written anything up formally, although I could if it seemed important.

-Philip White (philipjwhite@yahoo.com)