@Helios: it appears that at least Kemort did mean what he said and is wrong, so there you go.

ROFL, a weak attempt at divide and conquer isn't a proof either htrwin

Claim: 6 is not prime
Proof: 2*3=6
Q.E.D.

Is that better? Maybe you need to go back and look at what you guys were saying?

Very unconvincing since you've left out a lot so it doesn't read properly.

Nevertheless, you have shown by example, possibly without understanding it and definitely without following rigourous proof conventions, even by example, that 6 does not have the property of primality but said nothing about any number other than 6.

In fact, you have proved both helios and I are correct in saying a numerical example is not a mathematical proof.

You are now contradicting yourself htrwin

Where's your prof, as you go into the 'bottom of the barrel scrape'? We're waiting. Still making her macrame checkbook cover perhaps?

Claim: 6 is not prime Proof: 2*3=6 Q.E.D.

This is a proof of a property that applies to a set of size 1, and it's done by showing that the property applies to a single element. I.e. it does in fact apply to the entire set.

A statement of existence may or may not be provable by a single example.
The negation of "for all x in S, P(x)" is "there exists at least 1 x in S such that ¬P(x)". This statement is provable by a single example.
"There exist infinitely many x in S such that P(x)" cannot be proven in this manner. E.g. "there exist infinitely many twin primes".

Personally, I think both numerical proofs and arbitrary proofs are valid. I remember in high school, we had to prove certain mathematical concepts with only numbers, things like irrational numbers and logic. I am not taking sides here but I think both you guys sort of unfairly criticised UK Marine's way of proving a Linear Transformation. Although it may not be the most 'professional' way to providing proof, the patterns match and often times some teachers/professors may be satisfied with the result.

You are mistaken.

https://en.wikipedia.org/wiki/Collatz_conjecture#Statement_of_the_problem
https://en.wikipedia.org/wiki/Collatz_conjecture#Experimental_evidence

The conjecture has been checked by computer for all starting values up to 260. All initial values tested so far eventually end in the repeating cycle (4; 2; 1). [...] This computer evidence is not a proof that the conjecture is true. As shown in the cases of the Pólya conjecture, the Mertens conjecture and the Skewes' number, sometimes a conjecture's only counterexamples are found when using very large numbers.

https://en.wikipedia.org/wiki/P%C3%B3lya_conjecture

Pólya's conjecture was disproved by C. Brian Haselgrove in 1958. He showed that the conjecture has a counterexample, which he estimated to be around 1.845 × 10361

https://en.wikipedia.org/wiki/Mertens_conjecture
https://en.wikipedia.org/wiki/Skewes%27_number

No finite number of examples is sufficient to prove a statement about an infinite number of items. Anyone who claims otherwise has completely misunderstood mathematics.

Anyone who claims otherwise has completely misunderstood mathematics.

And they probably aren't very good at teaching macrame either.

I am not taking sides here

I think you are Multi

but I think both you guys sort of unfairly criticised UK Marine's way of proving a Linear Transformation.

What's unfair by revealing the truth. I think if there was any unfairness operating here it was by the alleged professor leading students to believe in a falsity. That's worse than unfair, it's borderline criminal. And before you thinks that's going over the top, consider the potential consequences for such irresponsible teaching at an alleged university for software in an emergency or mission critical system relying on sound mathematics.

Taken from https://www.math.utah.edu/~cherk/mathjokes.html

A lecturer:
"Now we'll prove the theorem. In fact I'll prove it all by myself."

How to prove it. Guide for lecturers.


Proof by vigorous handwaving:
Works well in a classroom or seminar setting.

Proof by forward reference:
Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.

Proof by funding:
How could three different government agencies be wrong?

Proof by example:
The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.

Proof by omission:
"The reader may easily supply the details" or "The other 253 cases are analogous"

Proof by deferral:
"We'll prove this later in the course".

Proof by picture:
A more convincing form of proof by example. Combines well with proof by omission.

Proof by intimidation:
"Trivial."

Proof by adverb:
"As is quite clear, the elementary aforementioned statement is obviously valid."

Proof by seduction:
"Convince yourself that this is true! "

Proof by cumbersome notation:
Best done with access to at least four alphabets and special symbols.

Proof by exhaustion:
An issue or two of a journal devoted to your proof is useful.

Proof by obfuscation:
A long plotless sequence of true and/or meaningless syntactically related statements.

Proof by wishful citation:
The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.

Proof by eminent authority:
"I saw Karp in the elevator and he said it was probably NP- complete."

Proof by personal communication:
"Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication]."

Proof by reduction to the wrong problem:
"To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem."

Proof by reference to inaccessible literature:
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.

Proof by importance:
A large body of useful consequences all follow from the proposition in question.

Proof by accumulated evidence:
Long and diligent search has not revealed a counterexample.

Proof by cosmology:
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.

Proof by mutual reference:
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.

Proof by metaproof:
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

Proof by vehement assertion:
It is useful to have some kind of authority relation to the audience.

Proof by ghost reference:
Nothing even remotely resembling the cited theorem appears in the reference given.

Proof by semantic shift:
Some of the standard but inconvenient definitions are changed for the statement of the result.

Proof by appeal to intuition:
Cloud-shaped drawings frequently help here.