Post me your hardest maths question you know

I understand the mathematical proof that 0.9r = 1 but I will never be convinced that the two are the same. We simplify 1/3 of 1 to 0.3r as it is impossible to represent it accurately.

Little point in continuing the discussion as I feel we are operating from different standpoints.

To summarise

Technically, 0.9r is not 1. Only 1 is one. The decimal representation of 1 is 1.0r.

1/Infinity represents an infinitesimal quantity, to use the term from earlier in the thread. It is approximately 0, but not equal to zero.

You can't say it equals zero because of the numerator; there is a 1 there, which denotes a quantity.

Don't get me wrong, I understand the reason that it is accepted that 0.9r equals 1, but in purely technical terms and precise math, it isn't truly equal.

You don't understand it then - mathematical proof is mathematical proof is mathematical proof - there is no 'technically' about it - it is likely your mistaken assumption that a non zero real number has a unique decimal representation that is throwing you off - it is the same number just represented differently.
 
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The guy on the left made a $10 profit but the guy on the right paid $50
 
You can't get a true answer from an infinite number as its impossible, even with infinite time and an infinitely complex calculator, no i think some of us understand infinity much better if anything.
I don't think you quite understand infinity properley yourself.
Infinity is neither a number, time or an amount.
 
Meh...


a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1


;)








Yeah I know it's incorrect, just putting it out there. :p

I know you said you know it's incorrect but for anyone who is wondering why it is

a = b
a - b = 0
a
and so when you divide the factor of (a-b) out you are dividing by zero. naughty naughty.
 
Here is a very hard problem that doesn't require any advanced mathematical techniques to solve, just a huuuuge brain!

There are N>3 gossiping women and each of them knows some item of gossip not known to the others. They talk to each other via the telephone and in each conversation they tell each other all they know at that point in time. What is the minimum number of phone calls required before each woman knows all the gossip.

Here is a simpler problem (still no advanced mathematics required):

I have a bowl containing 1000 strands of spaghetti. I pick two ends of spaghetti at random and tie them together, and I keep doing this until there are no more ends to grab. What is the expected number of loops in the bowl when I'm done?
 
I'll try desperately not to explode into a rant about 0.9r. Those with a long memory will remember my involvement with the first one....

Anyway.... Here's a vaguely accessible problem I had to solve today. 8 points in 3 dimensional space form a convex hull where all faces (of which there are 6) are convex quadrilaterals. What is the volume of the 3 dimensional hull? If you can't provide the explicit formula (and I don't blame you, its unpleasant) then provide the method by which you compute the volume and demonstrate it works for special cases like the hull being a regular cuboid. Extra points if your method work in any number of dimensions, not just 3 (though you'd be computing hyper-volumes obviously).
 
Here is a very hard problem that doesn't require any advanced mathematical techniques to solve, just a huuuuge brain!

There are N>3 gossiping women and each of them knows some item of gossip not known to the others. They talk to each other via the telephone and in each conversation they tell each other all they know at that point in time. What is the minimum number of phone calls required before each woman knows all the gossip.

Here is a simpler problem (still no advanced mathematics required):

I have a bowl containing 1000 strands of spaghetti. I pick two ends of spaghetti at random and tie them together, and I keep doing this until there are no more ends to grab. What is the expected number of loops in the bowl when I'm done?


1. is it n-1?

2. is it 1000! ?
 
Afraid not (to both). The first one is particularly difficult - it is given to Cambridge 1st year undergraduates in their first couple of weeks and on average I think the stats are that about 1 student every 2-3years solves it.

1 they have a multi way chat and they can do this because they can multi task.
 
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