Recent content by Alan1000

I've been debating (In a pub, where all of life's problems are solved) with a friend of mine, who's planning on becoming a priest after he finishes university, on his justification for believing in a god. He admitted that he had no proof for the existence of a god that isn't anecdotal, but that...

"I can never really make sense of sentences like this. What do you mean with "fraction approaching infinity?" A fraction is, and can never approach anything. It's the same as saying that 1 is approaching 2: it doesn't make any sense!" Micromass, I think we should both pretend you didn't really...

ey up lad, it's a recipe for bread pudding! doesn't tha know?

As a mathematical novice I have been following with great interest the recent debates (in more than one forum!) as to whether 0.999... = 1. The question is whether two ostensibly different natural numbers are equivalent, equal and synonymous. (I quote the three terms because mathematicians...

There are 10 kinds of people in the world: those who understand binary notation, and those who don't. Seriously though, I second the nomination of Pythagoras' Theorem. This was the earliest example of a genuinely profound mathematical insight, built upon axiomatic foundations which were...

Harking back to the original challenge: i.i=-1 is a definition, not a deduction; or to be more pedantically exact, i=sqrt(-1) is the definition which underpins it, and this means that the whole proposition is true "by definition", not by deduction. It is not at all the outcome of a...

Absolutely. It is my belief that Russell's greatness is not yet fully appreciated; we are still too close to him in time. Queen Victoria once said, "When I have dinner with Mr Gladstone, I feel as if I have spent an evening with the cleverest man in England. But when I have dinner with Mr...

And the definition of "axiom" is...? There are (broadly speaking) two basic definitions of the word "axiom". The classical definition, with which Plato, Euclid, and Aristotle wrestled, is roughly this: "An axiom is a proposition for or against which no evidence can be adduced, but the...

"At its heart, multiplication is a function. Say you have a set, F, of mathematical objects (it could be matrices, reals, integers, integers mod n, etc) then define the function M:(FXF) -> F by rule f(a,b)=c. Now, we are not given an explicit formulation for the multiplication rule..."...

I grant everything you say, Micromass. I set out to argue the case that the concept of 'multiplication' in ordinary arithmetic is not merely logically dispensible, it really does not exist, and I accept that I did not make my premises clear enough. And the occasional references to what we...

I guess I was unconsciously echoing Russell's comment about the cardinal numbers in the Introduction to Mathematical Philosophy. I agree it was a rash choice of words. But it was partly prompted by the fact that while quite a few people in this thread are asserting - and I emphasise the word...

"Of course, once you end up doing fractions, then the entire repeated addition story collapses... " I really don't think so, Micromass. Try it on piece of notepaper. If you try multiplying (say) one and three-quarters by five eighths, you will find that every step can be reduced to an...

I think some of you guys are confusing "non-intuitive" or "awkward" with "logically absurd". There is nothing logically absurd about adding something together "i" times; gongyae is right, it's merely non-intuitive. Same for 0.23 x 0.35; the equivalent addition is not absurd, just...

Was the Spitfire "area-ruled"? Any aerodynamicists out there? The Supermarine Spitfire, designed in the mid-1930s, supposedly enjoyed the highest mach rating of any propellor-driven fighter in World War 2. Even the Mustang, with its state-of-the-art laminar flow wing, could not match the...

Hi jarednjames, Thanks for that. I don't seem to have all the buttons you mention. Could this be something to do with Firefox/NoScript security settings, I wonder? I'll explore that possibility. Alternatively I might try (gasp) Internet Explorer...