Is it possible to find/construct any fraction on the number line, without “venturing out” in the 2nd dimension?

In essence, I’m talking about constructible numbers. The usual process is something like: https://i.ytimg.com/vi/q0UlaGctcwM/maxresdefault.jpg

… but that’s obviously ventiring out in the 2nd dimension.

We’re provided with a line and can obviously construct the integers with just a compass, because we’re allowed to measure the distance between 0 and 1 (or just pick any two dots as the unit distance) and apply that distance incrementally.

submitted by /u/avance70

So, I played a drinking game in which you play based on rolling a dice. Lowest number lost and had to take a shot, drink, or something like that based on the rules. I started wondering about the odds. What made me perplexed was the fact that equal numbers meant loss. So in a 1v1 a losing hand would be lower and equal to your opponent. Surely the odds must be equal because you both are in the same situation. But what happens when more players join, more specifically more than six players. Do the odds stay at 1/6 losing chance for the rest of the game, no matter how many joins, or is there some statistical shenanigans at play here? In my limited university statistic (I am only a filthy economist) I couldn’t remember a formula that covered that situation. Also, in my head I felt like after six players join, the odds for losing would be the same regardless, because of equal distribution. But boy, I feel so weird about it. Like somehow you should be marginally better of, hiding in the safety of the numbers.

Does anyone want to put my poor, uneasy mind to rest on the matter? 😀

submitted by /u/Sondrety

[Proof theory/Logic] Is there such a notion of a unique proof?

A proof is just a tuple of true sentences satisfying some condition. For any theorem, there exists many proofs for it.

But might there be some theorem in some logical system with exactly one proof?

Of course exact uniqueness wouldn’t be possible since one could arbitrarily insert a random true sentence among the tuple and it would still constitute a proof.

But for some theorem, is there some notion of a proof being unique up to X? (where X is something I’m not sure of yet… maybe homotopy equivalence in the sense of univalent foundations)

submitted by /u/mozartsixnine

what does ‘treat these proportions as “value of measurements” mean?

hi guys and gals,

I am working on a statistics assignment and im dealing with a data set about an experiment about an attention test. now i want to find out how three independent variables affect the accuraacy of the answer. i have the independent variables: condition = {control, dot, inverse} block = {1, 2, 3, 4} lag = {1, 2, 3, 6, 8}.

The assignment says ‘we treat the proportions as “values of measurements” ‘. i am just not sure what they mean by this. are they saying to treat ‘block’ and ‘lag’ as a continuous?

thank you

submitted by /u/mizunoseishin

What are the coolest “basic” math tricks you have learned?

Inspiration for this came from a recent reddit post that showed X% of Y is equivalent to Y% of X.

Full transparency, I am adult with kids and I never knew this equivalency was a thing – which is truly embarrasing and frustrating at the same time! I don’t recall this even being taught in my elementary school? Needless to say, I’ve gone all these years without having that helpful trick, and I don’t want my kids going through the same experience.

With that in mind, I’m curious about what other really useful math tricks/techniques each of you found helpful growing up. Focus here is basic math (e.g. mental math, quick on the spot calculations, simplifications of hard topics, transformations, etc.)

Key thing – just looking for basic concepts, not advanced ones.

Hopefully a quick change of pace from the crazy stuff I see all you posting about. FYI – love the sub, even if most of it goes whooshing over my head.

Thanks in advance (father of two young sponges)

submitted by /u/InFarvaWeTrust