Proof By Contradiction

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Expand view Topic review: Proof By Contradiction

Re: Proof By Contradiction

by Tdarcos » Sat Sep 02, 2023 5:28 pm

Yes, Paul got me to come back.

"Proof," as a concept, is often misused, because people are often unaware that for scientific evidence, except in mathematics, is never "proof"; it is simply evidence which supports the current hypothesis, or conclusion, of the particular theory or law to which it is related. A particular hypothesis becomes upgraded to a theory when overwhelming evidence confirms its premises. Any evidence that disproves it means it no longer deserves to be referred to as a "theory."

If the subject is mathematics, then a particular proposition can be "proven," by showing how the circumstances of that formula, concept, hypothesis, or conjecture, are always true, or always false.

A mathematical proposition, or scientific theory can, however, be proven wrong by showing a case or cases where it does not work, i.e. fails. For example, the hypothesis that water always freezes at 32°F or 0°C can be disproven by mixing salt into water and freezing it to where the temperature is less than that number, but the water is still liquid.

It's been said, anyone who wants to argue that the theory of evolution is not valid simply has to find just one example where it does not happen that way. (You would also win the Nobel Prize.) We actually have more evidence to support the theory of evolution than we do to support gravitational theory. It's about as close to proven as a theory is allowed to be referred to.

Re: Proof By Contradiction

by Paul Robinson » Sat Sep 02, 2023 5:02 pm

raecoffey wrote: Wed Aug 30, 2023 4:20 am Lmfao, where is he? Is he ok?
The guy is busy playing with his trains. That's not a euphemism, he downloaded and installed OpenTTD, an open-source clone of Chris Sawyer's Transport Tycoon Deluxe.

It's a sim where you get an imaginary world with towns, and industries, and you make money delivering things from one place to another, e.g. mail and passengers from town to town, iron ore to the steel mill, grain and livestock from farm to factory, etc. You then use the money to buy more trains/buses/trucks/ships/planes, build more stations, depots, docks, and/or airports, and lay track or roadways. You have four methods you can use: truck/bus, rail, airplane, and/or ship. Each has benefits, and drawbacks. Depending on the year, rail is railroad, electrified railroad, monorail, or magnetic levitation (Maglev). With an expansion pack (also free), you can also add vacuum-tube train (Vactrain). Does not require an account or log-in, and does not require Internet access, unless you want to download content created for the game by others. You play it the way people used to play computer games: off-line unless you want to play against others or download content. If you have no internet, that is (correctly) the only functionality you lose; the game can still be played normally.

I like the game, but I'm not a fanatic like TDarcos. Right now he's working on a map where two trains circle the edge in opposite directions. He wants to have two eight-car maglev passenger trains end up on the same track so they can collide with each other (like Gomez Adams does, only without explosives), at a combined speed of 500mph, killing over 500 people. I suppose he thinks that's fun; I don't know what the poor virtual passengers he plans to murder think about it.

If anyone is interested you can download and use OpenTTD for free from https://www.openttd.org. I don't recommend the version for Android, it's too hard to use the game controls.

I'll try to drag him away occasionally...

Re: Proof By Contradiction

by raecoffey » Wed Aug 30, 2023 4:20 am

Lmfao, where is he? Is he ok?

Re: Proof By Contradiction

by Ice Cream Jonsey » Tue Aug 29, 2023 8:30 pm

Well, to some extent we are waiting for the Commander to return and tell us we all got it wrong.

Re: Proof By Contradiction

by raecoffey » Tue Aug 29, 2023 8:09 pm

And... No one?

Re: Proof By Contradiction

by raecoffey » Sun Aug 27, 2023 8:59 am

Let me know if you get hung up with the notation.

Re: Proof By Contradiction

by raecoffey » Sun Aug 27, 2023 8:58 am

Re: Proof By Contradiction

by AArdvark » Sun Aug 27, 2023 8:56 am

I have no tea

Re: Proof By Contradiction

by raecoffey » Sun Aug 27, 2023 8:55 am

Ahh yeah and you can't do that without knowing the contrapositive technique, my bad. I'll get back with that one.

Proof By Contradiction

by raecoffey » Sun Aug 27, 2023 8:43 am

I have been thinking of how to introduce the concept of mathematical proofs and theorems to this board. You are all smart enough and capable enough to handle them. Basically, in grad school, you have to prove things Mathematically, and one of the ways is by contradiction. If you can find a contradiction that proves your theorem, them zap! ⚡

Give the algorithm a try. I have given you the shortest example that I could find

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