Pencils

[Bishop of Briggs]

Reminds me of a joke about a constipated draughtsman.

[ProfMoriarty]

[quote="marcelo"]



marcelo: I am intrigued (maybe even obsessed) with the above. Can you direct me to an internet website where I can get further information....maybe even add it for real to my own Christmas list....Hell, I might even just buy the damned get-up for myself. Thanks in advance for your help.
Jack

[ProfMoriarty]

[quote="marcelo"]



marcelo: would also appreciate any information you could give me on the pencil holder/extender above. Is this antique? How does it work? Again, thanks for your patience/assistance.
Jack

[marcelo]

marcelo: I am intrigued (maybe even obsessed) with the above. Can you direct me to an internet website where I can get further information....maybe even add it for real to my own Christmas list....Hell, I might even just buy the damned get-up for myself. Thanks in advance for your help.
Jack

Catalogue in PDF (in German):
http://www.faber-castell.de/bausteine.n ... =1010&fd=2

More information on the "Perfect Pencil":
http://www.graf-von-faber-castell.com/1 ... index.aspx

[NCW]

With 4 cms of pen left you need to make sure your nails are freshly cut lest you might scratch the paper.

I use a holder.

What matters in mathematics is the result AND the road to it. When I was in school the results were not taken into consideration even if they were correct if the way they were obtained was not on paper. Sometimes I would get half the points if my reasoning was correct, even if I had inverted a sign and the final result was wrong. We would also get extra points for deducing formulae in physics and mathematics rather than applying them directly from memory.

Absolutely. I was distinguishing between the point when the essential idea is seized, and the rigorous steps formulated, not meaning to imply that anything is done on supposition.

However, except geometry drawings, we were not allowed to write our examination papers in pencil and consequently I was used to writing everything in ink. If we made a mistake, it was part of our work: we would simply bar the faulty lines, put them between brackets and resume. If there was an early mistake, it was not acceptable to overwrite anything, as this increased the probability to make further mistakes. One thing I learned from my highschool math teacher, which also helped me in other situations life, is this: if you realize you've made a mistake at some point, don't hunt for it and try to modify what is already written: take a blank sheet of paper and start over. The same math teacher of whom we used to joke saying she was "convergent", according to a theorem which stated that in order for a series to be convergent it has to be bounded and monotonous...

In British school exams, I seem to remember the maths ones are the exception where you can write in pencil. I think, while it seems a nice idea to restart, replacing dropped factors or signs is by far the most common practice.

Your approach reminds me of Hardy, who was always acutely conscious of his middle-class background, and used to compensate in many amusing ways, enjoying the high life of a Trinity fellow. He used only the thickest creamy note-paper, and vast thick fountain pens, writing with exaggerated descenders; if there was a mistake or blot, however minor, he would scrap the entire sheet and start afresh, so that the day's work would always be a set of entirely clean, spotless arguments (to pidgeonhole to Littlewood, or suffer Ramanujan to copy with scrawled pencil onto the margins of newspapers).

You have the right idea with your statement of the result, but I think you meant to say that (real) bounded monotonic sequences converge, not the other way round.

[storeynicholas]

[
You have the right idea with your statement of the result, but I think you meant to say that (real) bounded monotonic sequences converge, not the other way round.

This kind of statement is just reason why I have never got beyond simple arithmetic. Please! what does this mean? Is there such a thing as an unreal bounded monotonic sequence? and, if so, how may it do anything?? Or is something else the other way round and, if so, what? It is as certain that you have the answer as it is that I shall not understand it and my brain will become even more knotted and confused than usual. However, let us see whether I can learn some mathematics today!
NJS

[NCW]

This kind of statement is just reason why I have never got beyond simple arithmetic. Please! what does this mean? Is there such a thing as an unreal bounded monotonic sequence? and, if so, how may it do anything?? Or is something else the other way round and, if so, what? It is as certain that you have the answer as it is that I shall not understand it and my brain will become even more knotted and confused than usual. However, let us see whether I can learn some mathematics today!
NJS

Sorry about that. Just restricting ourselves to real sequences, the original statement was that convergent sequences are bounded and monotonic; bounded is certainly (trivially...) true, but a convergent sequence is not necessarily monotonic. What I think was originally intended was to say that bounded monotonic sequences always converge, which is true. The implication only cuts one way: there are lots of sorts of convergent sequences; monotonic ones are just one sort.

Even though technically incorrect, it was unnecessarily pedantic of me to comment. General epistemological concerns are much more traditional for gentlemen's clubs, so I shall restrict myself in future to ideas of more general philosophical, and less technical, interest if the topic ever comes up again. I also apologise for hi-jacking the joke, which was originally genuinely amusing (and not one I had heard before), so thanks to Costi for that.

[storeynicholas]

I don't think that you hijacked Costi's joke as it made us laugh at the time. Now I understand that bounded sequences converge and that they may or may not be monotonic but I am still denied any understanding as to what they are: I just know how they behave (in this they resemble the fair sex) and I am seriously struggling with the concept of something being 'certainly' but only 'trivially true', especially when the denotation of a sequence does not necessarily include any other defining factor (as it need not be monotonic). I was not joking about the arithmetic.
NJS

[Atlantic Sailor]

When the occasional need for a pencil arises, I'm partial to my old Yard-o-Led rolled gold diplomat pencil. It takes leads that are a little too thick for extended mathematical work, but are just right for the quick sketch or short note.