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... 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

$\begin{pmatrix} \tilde\odot & & \tilde\odot \\ & \stackrel{\bot}{\smile} & \end{pmatrix}$
$B_4 i \sqrt u \dfrac {r u} {16}$

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...

For my funeral, I want an open casket affair.
I want to be dressed as Dracula, complete with costume fangs and theatrically-placed blood drips.
I want the ceremony to take place in the creepiest dankest spider-infested crypt that can be found.
I want the Catholic Mass to be performed backwards by a defrocked priest.
And finally, I want a stake hammered through my heart at the climax of the ceremony.

There once was a Yank in the UK
He'd been there since back in Y2K
While the girls made him smile
The food was quite vile
And the beer was utterly pUK

There was a young lady named Valerie
Who oft consumed many a calorie
Her clothing was roomy
Her health reports gloomy
And her food bill exceeded her salary

A Roger Waters parody

Isn't work horrid? Aren't I glad
That I don't have to do it.
Isn't time horrid? There's never enough
I must confess I blew it.
Isn't money horrid? But I don't care
I'm rolling in the stuff
Isn't war horrid? People say
I've said this often enough
Are you mental? So am I
And so's my old band friend
Every silly stupid thing
Will all come to an end.

What's THIS For ...!

Sandbox, In Progress, Later, Help Needed.

Keep chipping away ...


{{POTW Candidate}}



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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)

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)

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