I want you to think up the nastiest most challenging most pathological math problem(s) you can, and then i’ll try and solve it/them using the new method I’ve devised, one that involves manipulation of infinite numbers.

The problem(s) must be one of the three types:

• Limit of a sequence
• Limit of a divergent series
• Definite integral

But other than that, no limits on how pathological is it.

The problem may (but doesn’t have to) include, for instance, special functions, imaginary numbers, generalised functions, fractals, strange attractors, random numbers.

I’ll try to get an exact solution (even if the answer is some order of infinity) but if I can’t then will find a close approximation.

mollwollfumble said:

I want you to think up the nastiest most challenging most pathological math problem(s) you can, and then i’ll try and solve it/them using the new method I’ve devised, one that involves manipulation of infinite numbers.

The problem(s) must be one of the three types:

• Limit of a sequence
• Limit of a divergent series
• Definite integral

But other than that, no limits on how pathological is it.

The problem may (but doesn’t have to) include, for instance, special functions, imaginary numbers, generalised functions, fractals, strange attractors, random numbers.

I’ll try to get an exact solution (even if the answer is some order of infinity) but if I can’t then will find a close approximation.

Those i’ve tried successfully so far are the integral of tan(x) from 0 to pi/2, a sequence given by Henon attractor, a function that is 1 on the rationals and 0 on the irrationals, and the series 1 – 2 + 4 – 8 + 16 – 32 + 64 …

I haven’t yet tried the method out on special functions, imaginary numbers, or fractals.

So come up with something really nasty, please.

mollwollfumble said:

mollwollfumble said:

I want you to think up the nastiest most challenging most pathological math problem(s) you can, and then i’ll try and solve it/them using the new method I’ve devised, one that involves manipulation of infinite numbers.

The problem(s) must be one of the three types:

• Limit of a sequence
• Limit of a divergent series
• Definite integral

But other than that, no limits on how pathological is it.

The problem may (but doesn’t have to) include, for instance, special functions, imaginary numbers, generalised functions, fractals, strange attractors, random numbers.

I’ll try to get an exact solution (even if the answer is some order of infinity) but if I can’t then will find a close approximation.

Those i’ve tried successfully so far are the integral of tan(x) from 0 to pi/2, a sequence given by Henon attractor, a function that is 1 on the rationals and 0 on the irrationals, and the series 1 – 2 + 4 – 8 + 16 – 32 + 64 …

I haven’t yet tried the method out on special functions, imaginary numbers, or fractals.

So come up with something really nasty, please.

A bit out of my depth on this one, but I’d be interested to know what you get for Int(Tan(x)) between 0 and pi/2.

I get between 4.6 and 33.12, with 3 out of 5 results being in the region of 33.

I’ll go and see what the Internet says,

The Rev Dodgson said:

mollwollfumble said:

mollwollfumble said:

I want you to think up the nastiest most challenging most pathological math problem(s) you can, and then i’ll try and solve it/them using the new method I’ve devised, one that involves manipulation of infinite numbers.

The problem(s) must be one of the three types:

• Limit of a sequence
• Limit of a divergent series
• Definite integral

But other than that, no limits on how pathological is it.

The problem may (but doesn’t have to) include, for instance, special functions, imaginary numbers, generalised functions, fractals, strange attractors, random numbers.

I’ll try to get an exact solution (even if the answer is some order of infinity) but if I can’t then will find a close approximation.

Those i’ve tried successfully so far are the integral of tan(x) from 0 to pi/2, a sequence given by Henon attractor, a function that is 1 on the rationals and 0 on the irrationals, and the series 1 – 2 + 4 – 8 + 16 – 32 + 64 …

I haven’t yet tried the method out on special functions, imaginary numbers, or fractals.

So come up with something really nasty, please.

A bit out of my depth on this one, but I’d be interested to know what you get for Int(Tan(x)) between 0 and pi/2.

I get between 4.6 and 33.12, with 3 out of 5 results being in the region of 33.

I’ll go and see what the Internet says,

Internet says it doesn’t converge.

The Rev Dodgson said:

The Rev Dodgson said:

mollwollfumble said:

Those i’ve tried successfully so far are the integral of tan(x) from 0 to pi/2, a sequence given by Henon attractor, a function that is 1 on the rationals and 0 on the irrationals, and the series 1 – 2 + 4 – 8 + 16 – 32 + 64 …

I haven’t yet tried the method out on special functions, imaginary numbers, or fractals.

So come up with something really nasty, please.

A bit out of my depth on this one, but I’d be interested to know what you get for Int(Tan(x)) between 0 and pi/2.

I get between 4.6 and 33.12, with 3 out of 5 results being in the region of 33.

I’ll go and see what the Internet says,

Internet says it doesn’t converge.

It’s a bit of a bastard to calculate. I get this. log(2(ω+1)/π) where ω is the (infinite) number of natural numbers. There’s a slight cheat in this, but it’s not far off.

mollwollfumble said:

I get this. log(2(ω+1)/π) where ω is the (infinite) number of natural numbers. There’s a slight cheat in this, but it’s not far off.

I don’t get that at all at all.

But don’t let that worry you :)

The Rev Dodgson said:

mollwollfumble said:

I get this. log(2(ω+1)/π) where ω is the (infinite) number of natural numbers. There’s a slight cheat in this, but it’s not far off.

I don’t get that at all at all.

But don’t let that worry you :)

Yah, I’m more concerned about the slight cheat.