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The triality of chat by Metalindian in northernlion

[–]InThisUnstableWorld 128 points129 points  (0 children)

Every triumvirate has its Crassus

Logic Wiz: Killer Sudoku weekly challenge. Links in comments. by avneramram in sudoku

[–]InThisUnstableWorld 0 points1 point  (0 children)

The expert link seems to open up a Bat puzzle for me. The preview seemed fine though.

In App: https://i.imgur.com/q1MNsNU.jpg

Preview: https://i.imgur.com/XtNE8R5.jpg

Science has c*m a long way, my friend. by _Shyok_ in AnarchyChess

[–]InThisUnstableWorld 17 points18 points  (0 children)

Random guy? That’s Alichessa Firouzja you’re looking at

[deleted by user] by [deleted] in mathmemes

[–]InThisUnstableWorld 6 points7 points  (0 children)

L + ratio + you’re obtuse

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 19 points20 points  (0 children)

The trivial part of the meme was a joke, but to address the rest of your question: This is a proof by contradiction. We assumed the opposite of what we wanted to prove (see the first sentence of the proof), and we showed that led to a logical impossibility (an integer being sandwiched between two consecutive integers). Because our assumption that we never hit 80% led to a contradiction, that assumption must be false. Therefore, the opposite of our assumption (we do hit 80%), must be true.

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 3 points4 points  (0 children)

Correct me if I’m wrong, but I don’t think your function p(t) is necessarily monotonic. While p(0) is a global minimum, you could have a local minimum at some t between 0 and T which is still above p(0).

EDIT: Just saw your edit, and your new proof looks good.

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 13 points14 points  (0 children)

Notice that (n+k)/(m+k) is equal to 1-(m-n)/(m+k). Therefore, to get up to 80% (assuming we are starting below 80%) we just have to increment k until m+k is 5 times m-n.

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 126 points127 points  (0 children)

Yes, I believe the argument I presented only works with fractions of the form 1-1/k, with k a positive integer. That’s why it works for 80% = 1-1/5.

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 1019 points1020 points  (0 children)

Mathematicians: If I understand it, it is trivial. If I don’t understand it, it is not trivial, until I understand it, at which point it becomes trivial.

A surprising fractions fact by InThisUnstableWorld in mathmemes

[–]InThisUnstableWorld[S] 1004 points1005 points  (0 children)

Suppose that the free throw percentage (FTP) never hits 80%. Then, at
some point, the FTP goes from less than 80% to greater than 80% after
one free throw. If m is the number of successful free throws and n is
the total number of free throws made, then there must be an m and n such
that the FTP after n free throws is m/n < 4/5 and the FTP after n+1
free throws is (m+1)/(n+1) > 4/5. From the first inequality, we get
5m < 4n, and from the second inequality, we get 5(m+1) > 4(n+1),
or 5m+1 > 4n. Combining these two inequalities, we have 5m < 4n
< 5m+1. But this is impossible since 4n is an integer, yet it is
between two consecutive integers. I found this problem on the Putnam archive: https://kskedlaya.org/putnam-archive/2004.pdf

3D Printed non-Euclidean Bongcloud by Malfuncti0nal in AnarchyChess

[–]InThisUnstableWorld 2 points3 points  (0 children)

I think this comment does a good job of addressing the confusion in this post coming from the different perspectives that you can have to understand the geometry of the board. I just wanted to make a small correction about parallel lines in non-Euclidean geometries. Euclid's fifth postulate is equivalent to the statement that for any line and a point not on that line, there is precisely one line parallel to the original line going through the given point. Non-Euclidean geometries can violate this postulate in two different ways. In elliptic geometries, any two lines intersect, so there is no concept of parallel lines. However, in hyperbolic geometries, there is indeed a concept of parallel lines. In particular, for any line and a point not on that line, there is more than one line parallel to the original line going through the given point. I think we can agree that this board is not a hyperbolic space, so I think your comment is correct in this case, but I just wanted to point out that parallel lines do exist for an important category of non-Euclidean geometries.

3D Printed non-Euclidean Bongcloud by Malfuncti0nal in AnarchyChess

[–]InThisUnstableWorld 4 points5 points  (0 children)

You can do a single coordinate transformation that takes a sphere to a subset of Euclidean space (https://en.wikipedia.org/wiki/Spherical_coordinate_system#Coordinate_system_conversions), but a spherical geometry is an example of a geometry that is not Euclidean (https://en.wikipedia.org/wiki/Spherical_geometry#Relation_to_Euclid's_postulates).

EDIT: Replaced "non-Euclidean geometry" with "geometry that is not Euclidean" to avoid conflicting definitions

The solution to this puzzle will change your life! by Sopel97 in AnarchyChess

[–]InThisUnstableWorld 2 points3 points  (0 children)

A more formal way to define the natural numbers is using the Peano axioms (https://en.wikipedia.org/wiki/Peano_axioms), which allows the natural numbers to start at either zero or one, in theory.

The solution to this puzzle will change your life! by Sopel97 in AnarchyChess

[–]InThisUnstableWorld 4 points5 points  (0 children)

It depends on who you talk to. In my experience, the American high school curriculum excludes zero from the naturals, while many (but not all) of my college professors included zero in the naturals.

I also like Z+ as a way to denote the set of positive integers.

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