There's no controversy and no fallacy here — at least, not among people who actually understand basic number theory. Proper logic says you can't just "multiply everything by 10" because you get an infinite set of integers that you already used to count your first set.

Please describe "a multiplier and an offset" that maps the integers to the reals. (The reals, by the way, are not natural numbers.) I guarantee that whatever alignment you come up with, I can demonstrate a real number that is unaccounted for. The ironic part about your post is that you, in fact, are trying to apply…

Slight misunderstanding here. There are the *same* number of reals between 0 and 1 as all the real numbers together. But there are more reals between 0 and 1 (or any interval for that matter) than integers.

Again, a little humility goes a long way. Before posting that something is "stupid", take a moment to reflect whether (a) you have discovered something has eluded every mathematician since Cantor or (c) maybe you don't really understand this. (Hint: it's always c).

I'm sorry you guys don't understand this, but it's perfectly legit. And it's also the way it's taught in every math[s] course I've ever heard of. You shouldn't feel bad if this is confusing: in Cantor's time, when these ideas were first introduced, even mathematics professors of his day rejected his work. Having said…

Reality doesn't care whether you agree or not. Of course, you may mean "Internet agree with", which is a synonym for "understand".

Grammar nit: When Sam wrote "You've never heard of scopolamine" he meant "I've never heard of scopolamine". Sam Biddle: the Ric Romero of Gizmodo.

Rule zero of journalism: Don't write headline questions to which the answer is "no". It's a sure sign your article is dumb.

Actually... no. The universe can be both infinite and expanding, as crazy as that sounds.

Does anybody have a source for that quotation? I see it cited all over the Web, attributed to Einstein, but otherwise unsourced. And frankly, many of the quotes I see attributed to Einstein are obviously not his.

It's a Monday, the day Lifehacker shares tips gleaned from Friday's copy of Bored Housewife Weekly.

In today's edition of the Never Get Laid Again blog...

Did anybody mention the typo yet?

I have a pair of nice but inconveniently large Wharfedale Laser 80 speakers that I can't figure out what to do with (like this picture, except in good condition!). Any LHers have suggestions?

We've had 2-10 ever since we moved into this house, and I'd say it's more than paid for itself every year. There's been a couple of things where they said something wasn't covered that seemed marginal, but on the other hand when our AC unit failed for the Nth time and rather than repair it again I suggested I wanted…

One time I couldn't get Italian Arborio so I picked up American. How different could it be?, I thought. The answer is totally different. I will never make risotto with American Arborio again.

Who are you going to believe, a DARPA RFC or medieval monks?

Actual journalism on my Internet? It's more likely than you think.

I thought we'd agreed that it was OK for guys to want to kiss RDjr without it counting as gay? On the other hand, wanting to kiss Chris Hemsworth definitely counts as gay.

Here's the kicker: turns out we've *all* been trolled by an ex-Navy legislator who put the aircraft carrier thing in there purely to draw attention to the complete waste of time and money that this study represents. And it worked.