Search found 776 matches

by MartianInvader
Thu Oct 22, 2015 5:35 pm UTC
Forum: Mathematics
Topic: Convergence of sets in a geometrical sense
Replies: 27
Views: 4602

Re: Convergence of sets in a geometrical sense

So the amount of hand-waviness here is making me uncomfortable. Let me try to formalize what you're saying: Let A be a subset of R^n that can be expressed as a finite disjoint union of points and open balls. Then the "alternate Euler characteristic" of A is the alternating sum of the numbe...
by MartianInvader
Wed Oct 21, 2015 3:12 am UTC
Forum: Mathematics
Topic: Convergence of sets in a geometrical sense
Replies: 27
Views: 4602

Re: Convergence of sets in a geometrical sense

Okay, I think you and I have different definitions of Euler characteristic. What definition of Euler characteristic are you using here? The only one I know of that can apply to open balls (and the only one on the wikipedia page that can be applied to spaces that aren't finite cell complexes) is the ...
by MartianInvader
Tue Oct 20, 2015 10:59 pm UTC
Forum: Mathematics
Topic: Convergence of sets in a geometrical sense
Replies: 27
Views: 4602

Re: Convergence of sets in a geometrical sense

I believe arbiteroftruth's alternative proposal is exactly Hausdorff convergence (of closures); I was just pointing out it already has a name. Why do you want a shrinking set of circles to converge to the point in the center, but don't want the rationals to converge to the reals? They both seem to s...
by MartianInvader
Fri Oct 16, 2015 5:58 pm UTC
Forum: Mathematics
Topic: Convergence of sets in a geometrical sense
Replies: 27
Views: 4602

Re: Convergence of sets in a geometrical sense

I'm surprised no one has mentioned Hausdorff distance yet: https://en.wikipedia.org/wiki/Hausdorff_distance Caesar, I'm pretty sure your definition can be defined in terms of the Hausdorff distance. If the sets are all bounded, I think your limit is just the limit of their closures under the Hausdor...
by MartianInvader
Thu Sep 10, 2015 4:42 am UTC
Forum: Mathematics
Topic: I don't seem to understand my own brain teaser, please help!
Replies: 22
Views: 4762

Re: I don't seem to understand my own brain teaser, please h

The expected value is still 10*(1.235)^1000 days. However, this is made up of a very small chance of living a very long time, and a very large chance of living a very short time. Wait, isn't this wrong? If I win 55 times and lose 45 times I end up behind. Isn't the only valid way to do this with lo...
by MartianInvader
Mon Aug 24, 2015 8:40 pm UTC
Forum: Serious Business
Topic: Ethics of AdBlock
Replies: 639
Views: 110415

Re: Ethics of AdBlock

Using AdBlock has a "tradgedy of the commons" feel - each individual user doesn't change the overall ecosystem much, and improves their own personal experience. However, as more and more people use it, we're getting closer and closer to a day when an ad-supported internet is no longer sust...
by MartianInvader
Thu Jun 18, 2015 6:26 pm UTC
Forum: Mathematics
Topic: Why is 0! = 1?
Replies: 6
Views: 2287

Re: Why is 0! = 1?

To build on what Cauchy said, 0! means you multiply together all the integers that are bigger than 0 and less than or equal to 0 - but of course there are no such numbers, so 0! means "multiply nothing together", just like raising something to the zeroth power. The result of "multiply...
by MartianInvader
Thu Jun 18, 2015 6:12 pm UTC
Forum: News & Articles
Topic: 2016 US Presidential Election
Replies: 8482
Views: 930169

Re: 2016 US Presidential Election

My theory on Donald Trump is that he's running just to make the other Republican candidates look better. Kind of like last election where Romney seemed like a much more palatable candidate after the Ronpaul, Herman Cain, and Newt Gingrich had had their moments in the sun.
by MartianInvader
Wed Apr 01, 2015 9:18 pm UTC
Forum: Mathematics
Topic: Paths between two points
Replies: 18
Views: 3163

Re: Paths between two points

I feel like there's a use for Brownian motion here, but can't figure it out offhand - you could start with the Brownian distribution of paths starting at A, but the subset of those ending at B certainly has measure 0.
by MartianInvader
Fri Jan 16, 2015 9:21 pm UTC
Forum: Mathematics
Topic: What's This 'Almost Never' Probability Paradox Called?
Replies: 15
Views: 3854

Re: What's This 'Almost Never' Probability Paradox Called?

The name I'd give to this paradox is just "You can't divide by zero." You ask about the conditional probability of something when the condition has probability zero, and this probability is, by definition, 0/0. What you're saying is analogous to, "On the one hand this is what I get fr...
by MartianInvader
Thu Jan 08, 2015 9:34 pm UTC
Forum: News & Articles
Topic: Charlie Hebdo attack
Replies: 164
Views: 32071

Re: Charlie Hebdo attack

I think the actions of the extremists are completely rational here - their ultimate goal isn't tolerance of Islam, it's religious war. Everything they do that stokes the fires of hate, on either side (indeed anything that divides people into "sides" at all), moves them towards their goal.
by MartianInvader
Thu Jan 08, 2015 9:20 pm UTC
Forum: Mathematics
Topic: What is the biggest PWND you can get?
Replies: 10
Views: 2623

Re: What is the biggest PWND you can get?

Doesn't jaap's construction give as many points as you want, no three of which lie on the same circle (since all but one of them are co-linear)?
by MartianInvader
Wed Dec 17, 2014 12:02 am UTC
Forum: Mathematics
Topic: Sizes of Infinity
Replies: 60
Views: 12564

Re: Sizes of Infinity

The "size" of the real set in [1,2] is on the order of 10 n where n is the size of the counting set. The size of the real set in [0.5,1] is necessarily half of that because one of the digits is now restricted to be >=5, eliminating half the degree of freedom. Under the "bijection&quo...
by MartianInvader
Thu Dec 11, 2014 10:56 pm UTC
Forum: Mathematics
Topic: Sizes of Infinity
Replies: 60
Views: 12564

Re: Sizes of Infinity

0x783czar, the main issue here is that we need to nail down what we mean by "size". Size is really an abstract concept, and if we want to speak mathematically then we need to pin down this concept with a mathematical definition. The usual definition people use for the "size" of s...
by MartianInvader
Wed Dec 03, 2014 5:48 pm UTC
Forum: News & Articles
Topic: The Thread To Remind Me We're Living In The Future
Replies: 1798
Views: 275063

Re: The Thread To Remind Me We're Living In The Future

The "bots: no lying" form of captcha has now become a reality:

http://www.pcmag.com/article2/0,2817,2473062,00.asp
by MartianInvader
Fri Oct 24, 2014 11:08 pm UTC
Forum: Mathematics
Topic: Axis & Allies dice probability
Replies: 9
Views: 5445

Re: Axis & Allies dice probability

The chance of rolling 1,2, or 3 with no dice is .7^4

The chance of rolling 1,2, or 3 with exactly one die is (.3)(.7^3)*4

So the chance of rolling with at least two dice is 1 - .7^4 - (.3)(.7^3)*4 = .3483
by MartianInvader
Thu Oct 23, 2014 8:49 pm UTC
Forum: Mathematics
Topic: Non-contractible, simply connected subsets of R^n
Replies: 4
Views: 2127

Re: Non-contractible, simply connected subsets of R^n

I'm not sure I'm reading your notation correctly. Are you just ripping the end off the topologist's sine curve and pulling it around the circle? If so, keep in mind that at every stage of the homotopy, the image of every convergent sequence should converge to the image of its limit. For example, tak...
by MartianInvader
Wed Oct 15, 2014 9:56 pm UTC
Forum: Mathematics
Topic: fooling around with points on a plane and optimization
Replies: 7
Views: 3051

Re: fooling around with points on a plane and optimization

It'd be interesting to see how this problem behaved in higher dimensions. For example, in three dimensions, you can have 4 points with zero error, arranged in a tetrahedron. Similarly you can put n+1 points into an n-dimensional space with zero error, but I have no idea what the minimum error become...
by MartianInvader
Wed Oct 08, 2014 11:43 pm UTC
Forum: News & Articles
Topic: Microsoft to buy Mojang (aka Minecraft) for $2.5 Billion
Replies: 31
Views: 6884

Re: Microsoft to buy Mojang (aka Minecraft) for $2.5 Billion

Like when Google grabbed Motorola, before selling it overseas to the Chinese firm Lenovo? Google bought Motorola for $12 Billion, and sold it for $3 Billion. IE: Motorola is now worth around the same as Mojang. It's worth noting that Google sold the Motorola Home division separately to ARRIS for $2...
by MartianInvader
Tue Oct 07, 2014 7:01 pm UTC
Forum: News & Articles
Topic: Same-sex marriage now legal in 24 states
Replies: 54
Views: 12572

Re: Same-sex marriage now legal in 24 states

The argument, as I understand it, was that even though homosexuals have/had the same right to marry someone of the opposite gender as heterosexuals do, that they are being shorted because they can only be fulfilled, or can only love someone of the same gender. Well, let's stop there, since that's c...
by MartianInvader
Mon Oct 06, 2014 11:27 pm UTC
Forum: News & Articles
Topic: In other news... (humorous news items)
Replies: 14762
Views: 2217073

Re: In other news... (humorous news items, etc)

Yablo wrote: That's kinda like ignoring the zombies and guns in Resident Evil because they want the movie to be a romantic comedy, or ignoring the cars in Need For Speed and Gran Turismo because, damn it, those need to be westerns..

Obligatory link.
by MartianInvader
Mon Oct 06, 2014 11:23 pm UTC
Forum: News & Articles
Topic: Same-sex marriage now legal in 24 states
Replies: 54
Views: 12572

Re: Same-sex marriage now legal in 24 states

Notice how Right, and no one was previously allowed to marry the same sex, and everyone was allowed to marry the opposite sex. Equality for everyone! Notice how this argument implicitly relies on the person's gender, which is why it was considered unconstitutional under the 14th amendment? Where in ...
by MartianInvader
Tue Jul 22, 2014 4:19 pm UTC
Forum: News & Articles
Topic: Google tells music magazine to censor album covers
Replies: 44
Views: 9854

Re: Google tells music magazine to censor album covers

Well, it's not just protecting their brand, it's protecting their revenue stream. A lot of the advertisers who advertise with Google don't want their ads to run next to pictures of butts, and Google has chosen to keep their business (and, indirectly, provide more money for their safe-content partner...
by MartianInvader
Thu Jul 10, 2014 4:40 pm UTC
Forum: Gaming
Topic: Hearthstone
Replies: 590
Views: 114349

Re: Hearthstone

Oh I know it's used in other games - but in pretty much every one of those games, the mechanics you get out of the second deck are far more interesting than what you would get out of replacing lands with mana crystals. If you're going to add the complexity of a second deck to your game, you should b...
by MartianInvader
Wed Jul 09, 2014 9:15 pm UTC
Forum: Gaming
Topic: Hearthstone
Replies: 590
Views: 114349

Re: Hearthstone

I didn't mean it would be hard to *implement* in a physical game, just that it would be a pain to use. If you used a separate set of 10 cards for mana crystals, you're essentially now carrying around two decks. You'd have to be careful to keep them separate and not to accidentally shuffle a mana cry...
by MartianInvader
Tue Jul 08, 2014 11:04 pm UTC
Forum: Mathematics
Topic: Bad math
Replies: 88
Views: 16135

Re: Bad math

Wait, too many solutions to a polynomial implies there are zero divisors? I don't think that's true... what about the quaternions, where there are like 6 solutions to x^2+1=0?
by MartianInvader
Wed Jul 02, 2014 7:27 pm UTC
Forum: Gaming
Topic: Hearthstone
Replies: 590
Views: 114349

Re: Hearthstone

I've been playing this for a little while, and as a longtime player of Magic: The Gathering, I've gotta say I love how Hearthstone embraces the fact that it's played on a computer and not with physical cards. It drops things from Magic that don't work as well on a computer and adds things that would...
by MartianInvader
Wed Jun 11, 2014 12:33 am UTC
Forum: Mathematics
Topic: Vectors without components
Replies: 19
Views: 4430

Re: Vectors without components

Since no one has mentioned it, I'll throw in my favorite example of a vector space that has no "obvious" basis (and indeed requires AoC to even show there is one): The real numbers as a vector space over the rationals. It's pretty tough to think of that one in terms of "coordinates&qu...
by MartianInvader
Sun May 18, 2014 3:21 pm UTC
Forum: News & Articles
Topic: Google loses privacy case
Replies: 79
Views: 16250

Re: Google loses privacy case

There are special exceptions to the law for newspapers and other journalistic entities. Part of this ruling was that Google is not enough of a "journalistic entity" for these exceptions to apply. That's why the original paper didn't have to take down the notice but Google has to take down ...
by MartianInvader
Thu May 15, 2014 11:52 pm UTC
Forum: Mathematics
Topic: Bad math
Replies: 88
Views: 16135

Re: Bad math

Twistar: You are correct, the induction step fails at n=2. The language gets just a bit vague at that point (of course), so it's tricky to say exactly which statement is false. You could interpret "h has the same color as the other horses" to mean all horses besides the one tha...
by MartianInvader
Thu May 15, 2014 8:39 pm UTC
Forum: News & Articles
Topic: Google loses privacy case
Replies: 79
Views: 16250

Re: Google loses privacy case

I remember reading somewhere that Google has like 90% of the search market in Europe, so pulling out would definitely be felt. But it would be felt by Google, too, as they make huge amounts of money by showing ads to people in these countries. All in all, it would probably be easier for the EU to re...
by MartianInvader
Thu May 15, 2014 4:55 pm UTC
Forum: News & Articles
Topic: Google loses privacy case
Replies: 79
Views: 16250

Re: Google loses privacy case

The biggest danger in my mind is that it really threatens to just plain shut search engines down. If every request needs to be looked at by a lawyer to determine whether it's legit, even Google can't afford the huge number of lawyers it would need to process the claims from everyone in the world, le...
by MartianInvader
Wed May 14, 2014 9:59 pm UTC
Forum: Mathematics
Topic: Bad math
Replies: 88
Views: 16135

Re: Bad math

I've always liked the proof by induction that all horses are white: Theorem: For any (finite) set of horses, all of the horses are the same color. We prove this by induction on n, the size of the set of horses. Base case: n=1, obviously since there's only one horse in the set it has just one color. ...
by MartianInvader
Tue Apr 08, 2014 9:11 pm UTC
Forum: News & Articles
Topic: Brendan Eich steps down as Mozilla CEO
Replies: 874
Views: 76099

Re: Brendan Eich steps down as Mozilla CEO

What exactly is Heisenberg advocating here? A law that would force people to continue using a product if the only thing that's changed is their perception of an employee? Or a law that prevents companies from firing an employee if that employee's employment is hurting their business? Or some way of ...
by MartianInvader
Tue Apr 08, 2014 12:26 am UTC
Forum: News & Articles
Topic: US Supreme Court - Brought to you by Koch Industries
Replies: 84
Views: 11387

Re: US Supreme Court - Brought to you by Koch Industries

I wouldn't say dumping toxic waste chemicals into a river is an attempt to cause immediate harm either, but as more and more people do it, they damage and destroy important systems our country relies on. That's why you've got to regulate these things.
by MartianInvader
Sat Apr 05, 2014 11:08 pm UTC
Forum: News & Articles
Topic: US Supreme Court - Brought to you by Koch Industries
Replies: 84
Views: 11387

Re: US Supreme Court - Brought to you by Koch Industries

Guys... Free speech does not mean, and never has meant, that you can say whatever you want whenever you want. You can't threaten someone, you can't slander someone, you can't conspire to commit a crime, you can't yell "fire" in a crowded theater, and you can't spend more than a certain amo...
by MartianInvader
Tue Mar 18, 2014 5:02 pm UTC
Forum: News & Articles
Topic: Ukraine Crisis [New Title]
Replies: 891
Views: 146624

Re: Ukraine Crisis [New Title]

I think I mentioned it earlier, but the forced migrations/ethnic cleansings of the Crimean Tatars wasn't unjustified. There were constant uprisings since then; violence and hatred often breeds more violence and hatred. By the time of Stalin, sure, no Tatar had been around when they were enslaving E...
by MartianInvader
Mon Feb 24, 2014 4:54 am UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 32241

Re: Axiomatic mathematics has no foundation

I just wanted to correct a misconception you seem to have - around 99% of mathematicians don't really care about the foundational crisis, other than as an interesting story. As one of my professors put it, "If ZFC is proved inconsistent tomorrow, the logicians will sort it out and replace it wi...
by MartianInvader
Sun Feb 16, 2014 4:22 am UTC
Forum: Mathematics
Topic: Meta fundamental theorem.
Replies: 7
Views: 2911

Re: Meta fundamental theorem.

Do I need to know the fundamental theorem of fundamental theorems for the test?
by MartianInvader
Mon Feb 10, 2014 6:10 pm UTC
Forum: News & Articles
Topic: In other news... (humorous news items)
Replies: 14762
Views: 2217073

Re: In other news... (humorous news items, etc)

I guess they could have released the giraffe in the city. No lions there. Come on, you know no giraffe will be able to hold down a city job for more than a couple months. If we followed your advice, pretty soon all our streets would be lined with panhandling, crack-addicted giraffe hobos. In other ...

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