From ProofWiki
Jump to navigation Jump to search

Listen here, wolfchild ...

Information is not knowledge.
Knowledge is not wisdom.
Wisdom is not truth.
Truth is not beauty.
Beauty is not love.
Love is not mathematics.
Mathematics is the best.

Where do we go from here

... some useful $\LaTeX$ constructs
... and some proof structures
... and some stubs for journal citations
... and some $\LaTeX$ commands, alphabetical
... Alec Cooper's old date template
... and a cloud-based flowchart drawing package
... MediaWiki magic words
... List of Templates

$\begin{pmatrix} \tilde \odot & & \tilde \odot \\ & \stackrel \bot \smile & \end{pmatrix}$

What's THIS For ...!

Sandbox, In Progress, Later, Help Needed.

Keep chipping away ...


{{POTW Candidate}}



Edit tools


Source Work Progress

Number Sequence Progress

Unsourced pages (courtesy of User:StarTower)

Google Analytics

That which does not kill us makes us soggy and hard to light.

Please sign your posts.


In particular I need to look at:

"Some more advanced students (e.g., college seniors) use the implication symbol ($\implies$) as a symbol for the phrase "the next step is." A string of statements of the form

$A \implies B \implies C \implies D$

should mean that A by itself implies B, and B by itself implies C, and C by itself implies D; that is the coventional interpretation given by mathematicians. But some students use such a string to mean merely that if we start from A, then the next step in our reasoning is B (using not only A but other information as well) and then the next step is C (perhaps using both A and B), etc.

Actually, there is a symbol for "the next step is." It looks like this: $\leadsto$ It is also called "leads to," and in the LaTeX formatting language it is given by the code \leadsto. However, I haven't seen it used very often."

Such a distinction seems unnecessary, especially considering theorems such as Extended Rule of Implication. Surely at each step of the way we have an implied $\land$ going on everything before it? --GFauxPas 04:23, 12 February 2012 (EST)
Just a comment...I've seen $\leadsto$ to also mean "converges to" for sequences. Andrew Salmon 17:56, 12 February 2012 (EST)
Every notation has been used for more than one thing. The point is we need to choose one and stick to it. --prime mover 18:22, 12 February 2012 (EST)
What about $\therefore$, i.e. 'therefore' (given by \therefore)? It is relatively unambiguous, but little known/used. I have come to prefer words when other people have to read my work as well; in all other cases, $\implies$ suffices instead. --Lord_Farin 19:03, 12 February 2012 (EST)
I've seen cogent arguments elsewhere as to why not to use $\therefore$ but, shrug, do I care nowadays ...--prime mover 01:08, 13 February 2012 (EST)

Okay, see Definition:Distinction between Logical Implication and Conditional where I have laid down the law.

the generalization of the tarski-vaught test is also a standard statement of the theorem, and while slightly more general, it does not really require much more of a proof, hence the modication.--Yaddie 17:33, 6 March 2012 (EST)

... but as I say, please make the statement as a separate section of this page. As soon as I've finished what I'm currently doing I'll get onto it. --prime mover 17:36, 6 March 2012 (EST)


Tireless Contributor Barnstar.gif