/mg/ math general -- rational edition

No problems. Always happy to spread the wildpill.

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The actual (non-reddit) thread

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so implicit in the "..." notation is the statement that the ... is smaller in magnitude than a single unit of the last digit in the expansion, and this implies a position for the relevant number along the number line. is there really an issue with this? it seems like such a pedantic person could just as easily take issue with the introduction of the rationals.

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Yo I b liking math n shit. How do I memorize all the numbers like Einstein???

But wait. This means the number line is not continuous. As you move along the number line there are these discontinuities, like black holes, where the number lines goes off....fuck knows where...and then almost immediately resumes again like nothing happened.

WTF???

Ohhhhhh....my head is spinning. Going to lie down.

Woken up. That was a nice lie down. Lets see, where were we?

OMG! Our maths is like living in flatland!

FUCK! FUCK!

Been toying around with different ways of detecting the 2-adic valuation of 3n+1. Naive approach:

[math]\frac{3n+1}{2^{v_2 (3n+1)}} = -(3n+1) \displaystyle \sum_{j=0}^{\text{log}_2 (3n+1) +1} \frac{1 + 2\frac{4^j -1}{3}}{4^j} \sum_{h=0}^{2^j -1} e^{\frac{\pi i (2h+1)(3n+1)}{2^j}})[/math]

Second approach:

[math]v_2 (3n+1)= \text{min}_l : 1 - (-1)^{\binom{n + 2^l}{n} + l + 1} = 0 [/math]

that's actually not true, the rationals are dense or w/e terminology math uses: for any rational number you can find another arbitrarily close rational number. so we don't NEED the irrationals to construct the number line. but acting like we can't include them doesn't make sense to me either

>A number is a quantity that can be written down

>collatz conjecture
getting anywhere?

>we don't NEED the irrationals to construct the number line
Then what would [eqn] sup \{ x : x < x^{2} \} [/eqn] be?

It wouldn't be a real number of any kind you bumbling retard, because that set isn't bounded above.

It is true that the rationals are not a connected space, however.

[eqn]\left\{x \in \mathbb{Q} : x < x^2\right\} = \left\{x \in \mathbb{Q} : x < 0 \lor x > 1\right\}[/eqn] which has no supremum.

Nah, just found various restatements of the problem each with their own problems of either massive complexity or under-determination, e.g. this under-determined equation:

[math]3q_0 + 1 + \displaystyle \sum_{d=1}^{\infty} 2^{y_d} (2q_d + 1) \equiv 0 \in Z_2 [/math]

where q_d is the 'd'th odd number in the 3n+1 sequence from the odd starting point q_0, and y_d is the total number of divisions by two by that point.

>It is true that the rationals are not a connected space, however.
apologies for my ignorance of topology, but what does that even mean? it seems like the real number line is defined to be a connected space, that seems a little like begging the question & precisely the thing wildberger is bitching about...

>what does that even mean?
"Connected" means that a space cannot be partitioned into two nonempty disjoint open subsets. The usual metric topology on Q (which can be defined without reference to the real line) is disconnected, which reflects the fact that certain theorems (especially the intermediate value theorem) fail on Q.

>it seems like the real number line is defined to be a connected space
R is not defined as a connected space, but its definition is such that it turns out to be connected.

>that seems a little like begging the question & precisely the thing wildberger is bitching about
What wildberger seems to take issue with is whether the real numbers "exist" (whatever that means) or are "numbers" in his understanding of that word. The definition of the reals is not at all circular, but any argument about whether they "exist" (in either direction) is probably going to be.

At the end of this paper I suggested to search for correlations between the delay in particle experiments. My intention was urge the exploration of the idea that decay products can be categorized not only by angular correlations within the cylindrical particle experiment detectors, but also within temporal correlations. (delay prediction in final paragraph)
> Derivation of the Fine Structure Constant
> February 2012
> vixra.org/abs/1208.0076

A few months later this paper showed the first ever evidence of time reversal symmetry violation after they did find delay correlations in an old dataset from a major collider BABAR [pic related (A)]
> Observation of Time Reversal Violation in the B0 Meson System
> July 2012 :---->>>> [[[4 months to verify predicition]]]
> arxiv.org/abs/1207.5832

In this paper I predicted that there should be both positive and negative time modes in the universe not just positive. (Actually, I predict positive, negative, and null, just like the three time fields in Titor's C204 schematic)
> Dark Energy in M-Theory
> November 2011
> vixra.org/abs/1208.0077

In this paper some experimentalists pointed their detector a little further to the side of the energy spectrum in some quantum optics application and they did observe my predicted mode.[pic related (B)] Notice the odd note at the top of the first page of this arXiv submission.
> Negative frequency resonant radiation
> January 2012 :---->>>> [[[ 3 months to verify prediction]]]
> arxiv.org/abs/1201.2689

The negative freq resonant radiation group had a follow on paper. The unusual note at the top of the first page [pic related (C)] is there because all technical people know this experimental discover is HUGE!!!
> Soliton-induced relativistic-scattering and amplification
> November 2012
> arxiv.org/abs/1211.0256

Attached: TRINITY____+___mofdnjfgwe98rdddjyfd6stfyygyf8t9wueb5.png (1296x1096, 196K)

I also, predicted that the particle discovered at CERN in 2012, the so-called spin-0 "scalar boson" should actually turn out to be a spin -1 vector boson [pic related (D)]
> Quantum Structure
> February 2013
> vixra.org/abs/1302.0037

Attached: TINITY___PDG_Higgs.png (1276x1476, 533K)

nice result here. How come Veeky Forums-user ignores the usual recognition the heap on people who find nice results?

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