Counterexample Puns

Conjectures which have very large counterexamples like the one with Polya Conjecture.

I would like to know about some other conjectures...

Was working through some problem's and finally got the process of crafting counterexample's. It's very similar to finding bug's/hole's in software KISS goes a long way :).

Hi all,

I'm interested in getting a book of counterexamples in real analysis. As of now, I am considering this one: https://www.amazon.ca/Counterexamples-Analysis-Bernard-R-Gelbaum/dp/0486428753 but I haven't really heard of much discussion on a book like this and wanted to know if anyone had another book recommendation or suggestion.

Thanks so much:)

I've been thinking for ages of possible counterexamples that would make this statement false but I can't seem to think of one. Is the answer really false?

https://preview.redd.it/v1ejqbwbt4281.png?width=1062&format=png&auto=webp&s=5f977376569a29c3d0ca46d4b3f31665876c4cce

Thanks in advance! :)

Hi guys. I have spend all day searching for a story I heard while at uni.

It was some math convention in the mid century I think and a old professor scheduled a lecture on a conjecture of primality

When he starts, he goes up to the black board and multiplies two big numbers by hand. They are so big, it takes him 45 minutes to do it properly. At the end it shows the same number he initially wrote down, proving it's not a prime.

My question is: does anyone else know the story? Who is thus man, and what did he actually disprove?

Many thanks!

I've come across this rather convoluted problem:

Let X be a topological space, Y a hausdorff space, and f: X -> Y continuous. Let C be a closed subset of Y, and U an open subset of X such that U contains f-1(C). If X is compact, there exists an open neighborhood V containing C such that f-1(V) is contained within U.

The question now is: Find an example where X is not compact and such neighborhood V doesn't exist.

The fact that Y is Hausdorff prevents me from using the standard pathological counterexamples with discrete and trivial topologies. I assume that Y will then be some subset of the real numbers. X is not compact, so I've tried with different open and semi-open intervals for X, but nothing seems to work.

I've tried the standard pathological functions, Thomae's function, Dirichlet's function.. I'm really not sure what to do here. Any guidance would be tremendously helpful.

It can help prevent the listener from feeling defensive, and make them more open to hearing what you're actually trying to say.

In other words, does internalism or externalism support the counterexamples that stemmed from Gettier's analysis? Thank you so much!

Patient is a 70-ish female, remote history of endometrial CA s/p chemo and hyster, supposedly healthy otherwise (per outpatient records). She has been on metformin 500mg BID for quite awhile and states her PCNP told her that her blood sugar was "a little high but it's probably just from the chemo you had years ago". She's never heard the words diabetes/diabetic at any appointment, nor are they mentioned in her outpatient notes or problem list (our clinic and ED have an integrated EMR so I can easily see everything). She seems almost confused as to how she ended up in the ER because she "just had [her] annual visit and everything was fine".

Came to see me in the ED last night with complaints of n/v, fatigue, polyuria that had been going on "for awhile". You probably see where this is going even if you haven't finished or even started med school.

Blood glucose is close to 400, but normal AG. Massive glycosuria and proteinuria.I look back at her outpatient labs done about 5 weeks ago at her AWV, performed by NP (not in a FPA state).

Some highlights: Glucose ~350. A1C ~ 10%. Triglycerides ~700. Cholesterol >300. Her BUN/Cr were half of what they are now.

She was not on ANY lipid meds, and her only diabetic med was the metformin. No referrals, additional tests, or meds were ordered. Follow up plan was "1yr for annual and PRN".

I went back to talk to her and essentially try to find out what the fuck was going on. Told her about the grossly abnormal labs and she was stunned. She had not heard ANYTHING back about these labs that were resulted over a month ago. She just couldn't believe something like this could happen.

I know for a fact that all outpatient lab results are automatically returned to the workload/inbox of the ordering provider by the EMR, and they stay there until that provider responds to or closes the thread. In other words there's no room for human error (e.g. the lab lost the results, office staff didn't get a fax, results were sent to the wrong provider/office, etc.). The fact that I can see them in her chart means that they were sent directly to the NP that ordered them. (Even if there was some weird glitch, I can't see that excuse holding any weight in court. If you order a test, you'll like be held responsible for following up on the results regardless of whether said results are shoved in your face or require some digging to access.)

The only reasonable explanations are that either A) the NP never looked at the results, or B) the N

Show that for the equation 4x^(2n)-4y^(n)+1=r, where x,y are any positive integer with (g.c.d)=1, n>2 & x=/=y , "r" would never be a perfect power?

I've gotten to Seduction and have had to stop and reassess things for three days because this is jamming up my thoughts. I can't resolve it sober or otherwise but the last thing I want to do here is reinvent platonism. I'm posting here because I respect you guys a bit more than all of the other internet people.

(Whoops, double negative in the title)

Not all the skills require the lord to be in the colony's domain. The +4 cosmite per turn does require it. But the later production oriented unit cost reduction is always active.

So...for example I had a colony with a level 5 community wellness center, colony lord with that the production discount. and indentured contacts.

In one turn I was able to train four full stacks of indentured( 24 units total) and I'm pretty sure I could've done more but at a certain point I had to stop to conserve energy.

Hi, I think I've found a counter example for modus tollens (denying the consequent) and was hoping to verify here.

Modus tollens arguments are said to be logically valid; by that, if the premises is true, then the conclusion must be true too. The format is P→Q, ¬Q, │= ¬P. Or as words: if P then Q; not Q; therefore not P.

My example is this: If the visitor was a stranger, then the dog would have barked. The dog did not bark. Therefore, the visitor was not a stranger. However, even if the premise is true (the dog did not bark), that does not guarantee the conclusion (the visitor was not a stranger) -- what if the dog was drugged? The truth of the premise here did not eliminate other possibilities for the conclusion. Your thoughts are much appreciated.

My thoughts: >!I'm guessing that for modus tollens to work, it must be a possibility in truth for ¬P and ¬Q to happen, and given that, then it will work. But if it is not a possibility for ¬Q, then modus tollens does not work. That is, as its not possible for the dog to bark (¬Q) if it is drugged, then the modus tollens rule couldn't possibly give ¬P as a certainty.!<

Hi ! I know it’s maybe a dumb question but I have encountered it in several machine learning problems. Assuming you want to detect a particular word in a pronounced sentence.
1 - Is this a binary classification problem ?
2 - If so, what counterexample should I take for the class which is not the particular word ? (a set of random words ?) 3 - Is it possible to choose an optimal set of counterexamples to optimize the learning process
4 - Is it different according to the nature of the data (audio, nlp, images….)

Thank you for your help !

(Sorry for my English, it’s not my native language)

Fermats last theorem states a^n + b^n = c^n where n > 2 is insoluble with integers.

I recently rediscovered my old smart contract that would give a prize if you find a counterexample. https://etherscan.io/address/0x21b7637f29e2476c3d540219d8ab8b85b114c2b1

Finding a solution is obviously impossible since it has already been proved that no solution exists.

Just wanted to share this as I still think Ethereum could be used to create incentives for solving interesting math problems.

The Zero Lower Bound is also known as the moment when the rubber meets the road. Nominal Interest Rate on overnight deposits at the Central Bank and the equivalent short term government bonds pay out zero, zip, nada, nulla...percentage wise.

Many people attribute the fact that we are at the Zero Lower Bound to the top down decisions of Central Banks. It is them, in fact which decide the Nominal Rate on overnight loans between banks to meet the cash requirements to be held at the Central Bank per the regulations specifically put in place by the Central Bank itself.

Reality is that the Central Bank is not God. It has very little room for manouver and generally +/- 500bps the rate of interest on short term overnight loans is approximately the same as it would be without its intervention.

So if it's not the Central Bank driving the charge and being God establishing the rate, then who is it? Well It's us! It's us with our behavior and how we behave with our finances, most importantly how much do we spend and how our expenditure creates inflation.

Inflation is the rise of prices as measured in the unitary currency of controlled by the Central Bank of the country being examined. In the US the 2 indicators used by the Fed are the CPI and the PCE, those measure year over year, so when they are positive it means that there is, in fact inflation. When they are negative it means the phenomenon at play is deflation.

Inflationary and deflationary forces square off every day in the global and domestic economy to produce the result which is measured monthly by the aforementioned (CPI, PCE) indicators .

Now for inflation to happen there has to be a level of impulsivity which compels people to act on it and create a scenario in which money chases goods thus enabling vendors and retailers to rise the price. Matter of fact this is happening less and less and there are are some secular trends which favor deflation over inflation, they are just beginning to produce their effect upon the global economy :

1. Aging demographic, people become less impulsive as they age

2. Population (even young people) are increasingly risk averse compared to the past and you can see this everywhere, not only in finance, people live in the NOW less and less and thus are less impulsive, below some non financial trends

• a) Cigarette consumption is down

• b) Drugs consumption is down, especially stimulants

• c) Alcohol consumption is down

• d) ER visits due to bar brawls and domestic inj

The preprint posted last week has been withdrawn by the author: see his comment on the arXiv submission here. The main lemma in the paper---which the author called Theorem 1---was a statement in probability; according to the arXiv comment, a counterexample to it has been found.

I was looking through some of the old Conversation Threads and one of them asked about historical misconceptions, and the one I named was "Don't invade Russia in the winter" (since Hitler and Napoleon, the meme's main examples, both invaded in June. I also provided examples of powers that did fight Russia successfully during or through a winter). (1) Open Conversation and Trivia Tuesday for 30: All the little questions about the little things of life (and war) : WarCollege (reddit.com)

This made me think of the "Graveyard of Empires" moniker, and I wonder if it's just another historical meme that falls apart under scrutiny (i.e. "Russia in winter" can be debunked by just looking up the dates Hitler and Napoleon invaded, and something like "Don't fight a land war in Asia" is as simple as looking at literally any war in Asia that had a winner).

I reason that either there are successes that the meme is ignoring, or there must be more context to the British, America, and Soviet experiences than the "Graveyard" thing would imply.

Also, minor thing: does Reddit stop refreshing new posts as you scroll down? During my trip down memory lane I got stopped at posts just 5 months old. It wasn't just that I saw the posts loading (i.e. grey bars) and they weren't loading. It was like I had reached the end, even though I can still look up posts over a year old using the search bar.

What I'm getting at is, places where things other than what happened would likely have happened if BB were as rigged as a lot of people think it is.

Here are some counterexamples I can think of:

The reset week in BB16

If production were as interested in rigging the game for Frankie as people in this thread (which helped inspire this post) seem to believe, I'm not sure why production would let everything in the F5 transpire the way it did. They could have at least made the previous HOH immune in the reset week, for example.

Part 1 of the BB7 final HOH

It's no secret that America loved Janelle, and there are a couple of conspiracy theories about production helping Janelle elsewhere in BB7. However, this is a pretty obvious situation where I'm honestly not sure a single person would have complained if production had looked the other way when Janelle took her hand off. Honestly, I would have been tempted to look the other way (even as someone with no desire for rigging), as it's plausible Janelle didn't hear Erika's question, and it feels like a pretty "pedantic" thing to disqualify Janelle for that.

People who continue to relitigate the BB20 endurance comp and claim that production let Tyler cheat in it particularly need to answer for this counterexample, as the most obvious response to this counterexample ("they could have gotten sued if they looked the other way!") is not available to those people.

BB20's endgame/jury vote result

There are many times throughout BB history where there have been allegations and speculations of production intentionally influencing HGs in certain directions through the DR. This is a prime example, I think, of a case where we'd expect a different result than what we got had production been interested in that kind of thing.

People on e.g. Twitter love to talk about how much of a production pet Tyler was (and surely it's true to an extent), and for several obvious reasons it would have been better for the show had Tyler won BB20, so the motive would definitely be there. But even beyond that, I think it's plausible that the means would have been there as well. Sam in particular seems to be a juror who could have been fairly easily swayed if the DR were interested in nudging her into voting for Tyler; from what I recall, she wasn't a particularly bitter juror, she was jus

I was looking at "Proofs from THE BOOK" by Martin Aigner and Günter M. Ziegler. And I was wondering if there was a similar book consisting of nice counter examples for interesting conjectures. Any suggestions?

My attempt: So v_1, v_2, v_3, v_4 form a basis for V, which implies that any linear combination a_1 v_1 + a_2 v_2 is linearly independent. Any linear combination of that form must also be in U, as it is a subspace of V. Clearly U cannot have any linear combinations of the form a_1 v_1 + a_2 v_2 + a_3 v_3 + a_4 v_4, where a_3 and a_4 are nonzero, as that would imply v_3 and v_4 in U.

Therefore, a_1 v_1 + a_2 v_2 spans U, and it must be linearly independent, so it is a basis for U.

The is-ought gap, in Searle's own words, is the claim that "no set of descriptive statements can entail an evaluative statement without the addition of at least one evaluative premise". He challenges this claim with the following counterexample:

1. Jones uttered the words "I hereby promise to pay you, Smith, five dollars."
2. Jones promised to pay Smith five dollars
3. Jones placed himself under an obligation to pay Smith five dollars.
4. Jones is under obligation to pay Smith five dollars.
5. Jones ought to pay Smith five dollars.

One of my issues with this argument is something like the second objection addressed in the paper. I would phrase it as, "The argument rests on the hidden premise that "one ought to fulfill their obligations", and this is an evaluative premise. Therefore, Searle is deriving his 'ought' conclusion from at least one evaluative premise."

Searle's response to the second objection is this:

>I don't know whether 'one ought to keep one's promises' is a a 'moral' principle, but whether or not it is, it is also tautological, for it is nothing more than a derivation from the two tautologies:
>
>All promises are (create, are undertakings of, are acceptances of) obligations, and
>
>One ought to keep (fulfill) one's obligations.

I don't see how the fact (assuming it's true) that "One ought to keep one's obligations" is tautological refutes the claim that Searle is relying on an evaluative premise. I would expect him to show either that the statement is non-evaluative (which seems impossible to me), or that his argument doesn't rely on this statement to be true.

I think his response would require the following move:

1. The statement "One ought to keep one's obligations" is tautological.
2. [Something like "If a statement is tautological, then it is not counted among the set of premises from which the conclusion is derived"?]
3. The conclusion is entailed from a set of descriptive statements and no evaluative one.

I think it's most likely that I simply lack understanding of how logical derivation works, and haven't found a mistake by Searle. Maybe I'm severely misreading what Searle said! Please clear my confusion.