Almost Sure

George Lowther, Author of Almost Sure blog, on maths, probability and stochastic calculus.
Also on YouTube

[Almost Sure @Almost_Sure]

New YT video posted, on Wigner quasiprobability distributions

link below

[Almost Sure @Almost_Sure]

@Super6 Sol Campbell vs Argentina in 1998. Hopefully this time it won’t be disallowed!

[Almost Sure @Almost_Sure]

1990, England vs Germany penalty shootout

[Today in History @TodayinHistory]

If you could change the outcome of one event from history, what would it be?

[Almost Sure @Almost_Sure]

@stusfootyflash did he not like that?

[Almost Sure @Almost_Sure]

@FPLFella Not, not Sol Campbell's disallowed goal! I'd like to banish that from memory

[Almost Sure @Almost_Sure]

@simongerman600 asking for trouble

[Almost Sure @Almost_Sure]

You can also factor out the multiplication, but it’s the division that was the problem

[Almost Sure @Almost_Sure]

which is why games like Doom in the 90s only had textured horizontal and vertical surfaces, no slopes.
So in each horizontal or vertical line of pixels you only need one division by z-distance, which can be optimised out of the loop

[SudoX7 @sudox7]

division is 20-40 CPU cycles. multiplication is 4. if you're dividing by the same constant in a loop, you're paying that tax a million times for no reason.

one reciprocal. computed once. everything else is multiplication.

[Almost Sure @Almost_Sure]

@Joebenno @FBAwayDays Same for me. The drama, last minute comebacks, John Barnes rapping, World in Motion. The tears.
Not many goals though

[Almost Sure @Almost_Sure]

@afc_ben10 Colombia 1990 discovering that having a flamboyant sweeper-keeper nicknamed “El Loco” (the madman) can go wrong!

[Almost Sure @Almost_Sure]

that’s one country for me
Plus one I drove to, and drove back out without stopping the car, does that count?

[Troy Frasier AKA Revived Studios @RevivedThoughts]

Settle a debate I'm having.

Can you count having visited a country if you never left the airport?

[Almost Sure @Almost_Sure]

@FiPanther pretty basic, but no arguing with the speed of light!

[Almost Sure @Almost_Sure]

@FiPanther 1

[Almost Sure @Almost_Sure]

@DominikPeters it’s the same proof worded slightly differently, and proving the intermediate value theorem instead of just invoking it like I did

[Almost Sure @Almost_Sure]

Proving a basic statement in real analysis using different infinities

[Almost Sure @Almost_Sure]

@subcountability I think this proof method is good

[Almost Sure @Almost_Sure]

In fact, given subset S of ℝ, it is possible to construct a continuous nowhere constant
f: ℝ → ℝ
with extrema attained at exactly the points of S if and only if S is countable.
So, using (un)countability in the proof seems natural.

[Almost Sure @Almost_Sure]

In fact, given subset S of ℝ, it is possible to construct a continuous nowhere constant
f: ℝ → ℝ
with extrema attained at exactly the points of S if and only if S is countable.
So, using (un)countability in the proof seems natural.

[Almost Sure @Almost_Sure]

Proving a basic statement in real analysis using different infinities

[Almost Sure @Almost_Sure]

@subcountability I quite like the proof though. How else would you prove it?

[Almost Sure @Almost_Sure]

@subcountability I meant to use f\colon throughout, but stately typed f: in the preamble. And lemma as plural was just a typo. I did spot it at the last moment before posting but too lazy to fix, thinking no-one would notice or comment

[Almost Sure @Almost_Sure]

@gamray Islington Green at 9AM was still pretty bad, but will check later

[Almost Sure @Almost_Sure]

And I did have this question, glad Arsenal are paying for it

[Almost Sure @Almost_Sure]

Looking lovely out

[Almost Sure @Almost_Sure]

to be fair, they are now cleaning up

[Islington Council @IslingtonBC]

Our teams are working hard to clean up after yesterday’s @Arsenal parade – and what a day it was!

With over a million people attending, it’s a major clean-up. We’re getting through it as quickly as we can, so please bear with us while we get the borough back to its best ✨ (1/2)