Thanks for the bedtime reading!

I mostly deal with foundations of analysis, so this could be handy.

Ehh, completed infinities give me wind…

Reals are just point cores of dressed Cauchy sequences of naturals (think of it as a continually constructed set of narrowing intervals “homing in” on the real being constructed). The intervals shrink at the same rate generally.

1!=0.999 iff we can find an n, such that the intervals no longer overlap at that n. This would imply a layer of absolute infinite thinness has to exist, and so we have reached a contradiction as it would have to have a width smaller than every positive real (there is no smallest real >0).

Therefore 0.999…=1.

However, we can argue that 1 is not identity to 0.999… quite easily as they are not the same thing.

This does argue that this only works in an extensional setting (which is the norm for most mathematics).

Extra fact - in the USA almost all games use long weighted reels.

I believe this is by law, but may be misinformed.

Also, if you know the rng gen you can game machines: a very very clever group in Russia bought up old machines from defunct casinos, reverse engineered the games, and then developed an app that let a user photograph x number of spins to find out what the seed was for the next spin, and from there told them to bet high or low based on the upcoming game. They made millions, and farmed it out to make more. (https://www.wired.com/2017/02/russians-engineer-brilliant-slot-machine-cheat-casinos-no-fix/)

Never really worked with them (we never made them).

I think they’re lower prize threshold cat Bs.

In the UK, slot machines fall into 4 main categories. Of particular interest are category C machines, as these can remember a fixed number of previous games. I.e. the “myth” that a machine is “about to pay out” because “someone lost a lot to it” can hold for these games.

Cat A and B machines are completely random, previous games can have no impact on probabilities of winning (though pots can climb).

Online games have different rules, not always fair ones!

Oh, and ALL games (in a physical location) must (by law) show “RTP” (return to player) somewhere. It usually gets stuck it in a block of text in the manual since no-one reads them. (If it’s below 97.3% just go play roulette as it offers better returns).

https://www.youtube.com/watch?v=-Im4YAMWK74

Relevant follow-up (videos explore Korean gender politics and hierarchical society).

Wow… They want to give AI even more mental illness and crippling imposter syndrome to make it an expert in one niche field?

Sounds like primary school drop-out level thinking to me.

Capitalists AND Reviewer 2… Never underestimate the power of Reviewer 2 in publication!

“How do we stop the world’s smartest people from realising what we’re doing?”

“Let’s make them fight among themselves and call it a meritocracy; we’ll limit their funding and let them keep themselves busy with political infighting!”

Media praising bikes - “Bike brain goes brrring brrring!”

Media criticising bikes - “Car brain go vroom vroom vroom!”

Come now, let’s be fair and open minded ;)

Oh the media often goes both ways - in this case it appears that there are some issues that need resolving. Not everyone appreciates dodging bikes mounting the sidewalk, or doing an emergency stop when cyclists dismount the pavements without clear signaling - this is a problem for everyone but the person on the bike. Cars have their own issues, and those are widely covered.

While I very much agree every media story has “spin” (be it unwarranted cynicism or blind optimism), I am fairly certain it is the same on both sides of this issue.

Your point seems to be “all good things on bikes are backed up by studies, all bad things about bikes are big oil”, and that is quite simply the best validation of my post you could ever give. Thank you.

Media praising bikes - “Look see they work”

Media criticising bikes - “Huh, would you believe the media spin right?”

Hah, jokes on them, my university is too poor to afford copilot.

Definitely the wrong argument against bikes.

A lot of the best ones just come down to time - 30 mins commuting in traffic vs 70+ cycling. 1-2 grocery trips per week vs 4-6.

Good public transport can balance that out (though less so for shopping).

And, as a mathematician who has been coding a library to create scaled geometric graphics for his paper, I hate -0.0.

Seriously, I run every number where sign determines action through a function I call “fix_zero” just because tiny tiny rounding errors pile up in floats, even is numpy.

So about 3150 pints of blood (10.5 being average for an adult).

Sounds doable XD

Edit: New ethical dilemma just dropped - kill 300 to forge the sword, or deny 3150 people blood in an emergency to forge the sword…

I have a rare medical condition that makes my coughs sound like “scihub” and “libgen” around undergrads.

I would like to investigate it further to seek a cure, but sadly the medical journals I’d need access to are paywalled. Oh well.

I mean, here is a thought, if an AI tool uses creative commons data, then it’s derivatives fall under creative commons. I.e. stop charging for AI tools and people will stop complaining.

I’m arguing from the standpoint that we establish the idea of counting using the naturals - it’s countable if it maps to the naturals, thus the link. Apologies for the lack of clarity.