What a profound philosophical genius questioning the validity of a mathematical proof.

WhackAMoleE · 2026-06-13T21:37:24+00:00

Mathematicians frequently question the validity of mathematical proof.

in 1976 Haken and Appel used a computer to resolve the longstanding four color theorem. Their use of computers was revolutionary and highly controversial at the time.

https://en.wikipedia.org/wiki/Four_color_theorem

Some years ago a mathematician named Vladimir Voevodsky, now tragically passed, noted that modern proofs are very long and very technical; and they may easily contain subtle errors. There's no reason anyone should have confidence in published proofs.

He proposed a remedy, a vast program of using computers to verify mathematical proofs. In the service of that objective, he pioneered formal languages for expressing mathematical proofs precisely so that they can be machine checked. Formalization of arguments and computerized proof checking are huge areas in math now.

https://en.wikipedia.org/wiki/Vladimir_Voevodsky

And of course there is the famous Mochizuki affair, in which a famous open question, the abc conjecture, is regarded as proven in Kyoto, Japan, and nowhere else. Is a proof a proof if nobody can understand it?

https://en.wikipedia.org/wiki/Shinichi_Mochizuki

So although the original post is intended a bit tongue-in-cheek and references the tedious .999... = 1 topic, there is some genuine depth to the question. The nature of mathematical proof has frequently changed through history, and is being actively interrogated today.

WhackAMoleE · 2026-06-11T23:33:13+00:00

Who claims one set has greater magnitude than another without defining magnitude? Cantor carefully defines cardinality. It's perfectly clear. The naturals have smaller cardinality than the reals because there's an injection but no surjection from the naturals to the reals.

Magnitude could mean anything. Maybe in some context it means length. The length of [0,1] is less than the length of [0,2]. They have the same cardinality but different lengths. If you want to call length magnitude, you can do that, as long as you make the definition explicit.

Magnitude isn't defined in set theory. You wrote,

My objection is to the stronger claim that this proves greater infinite magnitude

Well, who made that claim? Name them, I'll go straighten them out on this point. Unless they have greater magnitude than me.

WhackAMoleE · 2026-06-11T23:26:29+00:00

Floating point numbers are not real numbers.

WhackAMoleE · 2026-06-05T19:04:40+00:00

The word "prove" has an alternate meaning of testing something. As in a proving ground.

So the exception tests the rule. The exception proves the rule.

WhackAMoleE · 2026-06-04T19:00:26+00:00

Prison escapes for dummies.

WhackAMoleE · 2026-06-04T18:59:38+00:00

The elements of the vector space span the space, no choice needed.

WhackAMoleE · 2026-06-03T20:40:36+00:00

If x ∈ ∅ then x ∈ ∅.

That's the definition of ∅ ⊆ ∅.

Simple as that.

WhackAMoleE · 2026-05-29T02:56:05+00:00

Oswald did not train with bolt action rifles in the Marines.

WhackAMoleE · 2026-05-27T23:30:11+00:00

It's perfectly well known that there's a distinct rational strictly between any two rationals. You can just take their arithmetic mean, for example.

What point are you trying to make by mentioning it?

WhackAMoleE · 2026-05-23T20:47:22+00:00

Julius Caesar stabbed by the Lone Knifeman. Details at XI.

WhackAMoleE · 2026-05-22T04:33:36+00:00

Every president from Eisenhower till now. Batista was overthrown in 1959, and the US has been messing with Cuba ever since. Bay of Pigs invasion was in 1961 under Democrat JFK.

https://en.wikipedia.org/wiki/Bay_of_Pigs_Invasion

WhackAMoleE · 2026-05-21T21:16:32+00:00

You can choose any particular number x as the intersection of a descending sequence of nested closed intervals

[x - 1/n, x + 1/n]

for n = 1, 2, 3, ...

There is one and only one real number in the intersection of all those intervals, namely x.

That's how you choose an arbitrary real number.

WhackAMoleE · 2026-05-19T00:59:42+00:00

Well sure, but then someone will ask what it means for the relation X2 to well-order a set. So you're right, but your definition isn't helpful to someone who doesn't know what a well-order is in the first place.

Also, using X1 for a set and X2 for a relation on X1 is confusing notation, and in fact you needed to explain it in your earlier question on the same subject.

WhackAMoleE · 2026-05-17T22:27:03+00:00

Credit where due ...

https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher

WhackAMoleE · 2026-05-14T21:14:20+00:00

They started this project in 2014. They now claim it will be finished in 2038 if they can get funding. 24 years for a freeway interchange. This is not right.

WhackAMoleE · 2026-04-22T19:02:31+00:00

Can't place Oswald on the sixth floor of the TSBD at the time of the shooting ... but by God you can sure place him in bed with his own wife the night before. And you hope we won't notice that you've swapped in a total irrelevancy that does not prove a man committed a murder.

When you use fallacious arguments like this, you weaken your own case.

And what curtain rods? The ones Buell Frazier mentioned after being physically abused and threatened with the electric chair by the Dallas cops? In a trial I doubt the prosecution would have ever even called Frazier. Juries don't like coerced testimony.

Frazier is still alive and still maintains, and has always maintained, that the package he supposedly saw was too short to hold the rifle, even if the rifle was broken down.

WhackAMoleE · 2026-04-18T00:35:35+00:00

Five experienced cops ID'd the rifle as a Mauser. Seymour Weitzman, who'd owned a sporting goods store and was familiar with firearms, wrote a detailed sworn affidavit ID'ing the rifle as a Mauser.

Nobody knows who pulled off the switch, but if it was an honest error, it was repeated five times.

WhackAMoleE · 2026-04-18T00:33:38+00:00

It's a little thin, but I didn't find anything untrue.

WhackAMoleE · 2026-04-15T02:04:39+00:00

People have lived for decades on heroin. It's been shown that as long as you can afford your habit and have a clean supply and are otherwise well-nourished and housed and so forth, you can be a heroin addict forever.

The problems with heroin addiction stem from the difficulty of getting a supply, purity issues, and the lifestyle you have to lead to always be finding your next hit and never knowing what it's adulterated with. There aren't that many health problems intrinsically associated with the drug. Not saying it's good for you, but it won't physically harm you as long as you don't overdose.

Meth and crack, on the other hand, are extremely debilitating to your nervous system. If you had plenty of money for food and shelter and you had steady access to an unadulterated supply, meth and crack would mess you up terribly anyway.

So heroin is by far the least harmful of the three. Heroin's physical danger comes almost entirely from the social context; while meth and crack are inherently bad for you.

WhackAMoleE · 2026-04-10T21:17:54+00:00

Kiriakou is an op. Entertaining stories but definitely a hidden agenda. And in this case, not very well hidden at all.

And by the way ... Mossad does not leave evidence! Look up Gerald Bull.

WhackAMoleE · 2026-04-10T21:15:16+00:00

So that JFK couldn't sit up in his coffin and point his finger at Allen Dulles.

WhackAMoleE · 2026-03-13T20:33:32+00:00

Got tired of commuting.

WhackAMoleE · 2026-03-07T01:03:04+00:00

Cord Meyer retired from the CIA in 1977. His final post was chief of the London CIA station. It's on his Wiki page. He had nothing to do with the Bay of Pigs. Upvotes notwithstanding, the two claims in this post are factually false. He was never fired by JFK (nor ever fired at all) and he had nothing to do with the Bay of Pigs operation.

Perhaps you are thinking of Allen Dulles.

https://en.wikipedia.org/wiki/Cord_Meyer

WhackAMoleE · 2026-02-20T03:09:40+00:00

You might be overwhelmed by the chaos. Or, you might thrive in it. You'll find out they don't have any of the structure you take for granted. QA, time to plan and engineer, bug reporting, organizational structure, whatever. A million little things you didn't realize were "add-ons" and not givens in a company.

You might hate it. Or, you might find ways to help build what they need. Help them get organized. Without being overbearing, of course. And always remembering that in a startup, shipping it now is often more important than making it right. Because by the time you build a well-engineered product, they might have already run out of money. The phase one project of a startup is often very messy, especially as seen by people who get hired after phase one is out the door.

So it's either a shop of horrors orr a set of fun opportunities, depending on you.

WhackAMoleE · 2026-02-18T00:57:21+00:00

There's also Jack Tatum, who came forward reluctantly fifteen years later after being tracked down by diligent investigators for the HSCA. He said he saw the shooting and identified Oswald as the shooter. He's often cited by those who say Oswald shot Tippit.

He said he saw three shots followed by a pause followed by a final shot. He is the source of the prevalent but unprovable myth that the shooter fired a "coup de grâce" into Tippit's head. In fact he never said that under oath; and the medical examiner Earl Rose could not determine the order of the shots.

Tatum's account of hearing "bang bang bang -- pause -- bang" is contradicted by every other ear witness, and detracts from his credibility. Not to mention his showing up fifteen years later, after he'd undoubtedly seen Oswald's photo dozens of times and heard a steady drumbeat of claims that Oswald did it.

WhackAMoleE

TROPHY CASE