Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions

Revision as of 18:52, 4 May 2009

Revision as of 09:36, 5 May 2009

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**::Well, if you'd still like to stick with "numbers" rather than "integers", how about this: "Thus, Euclid's algorithm, which directly computes the GCD of two numbers, can be used to calculate the GCD of any group of numbers, regardless of the size of the group." Or something? As long as we avoid phrases like "number of numbers", it should be fine. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:52, 4 May 2009 (UTC)

**"This approach begins by showing that, if the theorem holds for n, it also holds for n + 1." I just learned about induction last semester, and this doesn't seem to be quite right, specifically the last two clauses. My understanding of induction is that it is a two-step process. The first step is proving the basis case (usually n=0 or n=1), and the second step is proving that it holds for n+1. The sentence in question is written as though the first step proves the second step, which is not the case.

:::For induction, it doesn't matter whether you prove the basis case first and the (''n'' implies ''n''+1) step second, or the reverse. I chose to present the method in the reverse order because (1) I thought it would be easier for lay-people to follow, (2) it emphasizes the (''n'' implies ''n''+1) step, which I feel is more important; and (3) it de-emphasizes the basis case and clarifies that a proof could start with any basis case, e.g., ''n''=7. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:36, 5 May 2009 (UTC)

**"A recursion is an equation relating numbers that form a series a1, a2, a3, etc." This is a very poor definition of a recursion, as it does not adequately explain the concept to a reader with no prior familiarity to it. How about "A recursion is an equation in which ''a_n'', an arbitrary term in a [[series]], is defined by the values of previous terms in the series, such as ''a_n-1'' or ''a₀''". This will also help the reader understand the Fibonacci example a bit more clearly.

:::That's a good suggestion. I've re-worded the recursion along these lines. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:36, 5 May 2009 (UTC)

**"Several equations associated with the Euclidean algorithm are recursive, such as ''r''_''k'' = ''r''_''k''−2 − ''q''_''k''''r''_''k''−1." This example is essentially useless, as neither the meaning of the equation nor the terms used therein have been defined yet.

:::Eliminated foreshadowing. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:36, 5 May 2009 (UTC)

**"Finally, in infinite descent, a given solution is used to construct a smaller solution." I read this sentence and thought I understood the concept being explained. Then I read [[infinite descent]]. Then I reread this sentence, which I now realize does a fairly poor job of explaining infinite descent. My familiarity with the concept is limited to that which I have just read, so I have no suggestion as to how to concisely summarize it, but I strongly urge you to rework the current explanation.

::: I hadn't wanted to talk about the (more common) use of infinite descent in impossibility proofs such as [[Fermat's Last Theorem]]. Rather, my goal was to prepare the reader to follow the logic of why the EA must stop eventually. Nevertheless, I've re-written those sentences to to give a broader understanding of the argument. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:36, 5 May 2009 (UTC)

* More to come. Good work thus far. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)