The infinity of all real numbers is larger than the infinity of all natural numbers.
http://en.wikipedia.org/wiki/Aleph_number
(this probably isn't very helpful, but it's how mathematicians quantify the "bigness" of an infinity)
Regardless,
No. Infinity doesn't surpass the "bounds" of mathematics. For god's sake, we construct infinities mathematically! The universe we see isn't infinitely large; infinity only EXISTS inside mathematics, but that doesn't make it any less powerful and "real" of a concept.
At no point do the "laws of mathematics" have to "round up". Unlike physics, mathematics has no "planck length"- it can deal with arbitrarily large infinities. It may seem really freaking weird, but there you go.
It depends on the infinity you're talking about. You can use something like mathematical induction to demonstrate 9.999... -
9 - 0. = 9
9.9 -
9.99 -
9.999 -
etc. Is there any finite number of 9s you can tack on to make this not true? No- and there's no reason an infinite number of them will make any difference to it.
9.99999...
-0.99999...
=9.000000...
Or,
9 + (
Algebraically rearranged- you CAN do this:
9 + (.9 -
How can you multiply pi by anything at all? After all, not only does it have an infinite number of digits, we don't even know what they all are!
How can you multiply 1/3 by anything at all? 1/3 =
How can you multiply 1 by anything at all? After all, 1 = 1.000000... which is an infinite number of 0s.
.999... is not an infinite number. It's finite in the same way pi is finite, and 10*pi - pi = 9*pi. It's a decimal expression of an infinite series, though.
9 + 9/10 + 9/100 + 9/1000 +
Everything after 9 cancels out (9/10 - 9/10, 9/100-9/100...) so you get 9 exactly.
Yes. Soviet-era Russia, Iran, and Iraq were/are all as bad as this. Detaining a dissident and his family is hardly the worst thing any of them did.
It's not stupid- it can be pretty damn effective (see: Aung San Suu Kyi).
No, that's not what they're saying. It's not about breaking RSA or whatever- strong cryptography is a requirement of, but not sufficient for, an unhackable voting system.
As long as you're right handed, anyway. I looked into fountain pens and they're very difficult to use with your left hand- the ink smears unless you write in bizarre orientations.
I read about a study where they hooked a guy up to sleep monitors, and whenever he looked like he was going into REM sleep they'd poke him or play a noise or something, just enough to get him out of REM sleep. He'd wake up in the morning feeling well-rested, but exhibited a lot of the same symptoms as someone seriously sleep deprived.
Out of curiosity, what would a proper electronics geek do to find one/disable of those things if he knew it was in the room- short of tearing everything apart? Is it possible to rig up some sort of detector that could find it- or some sort of electromagnetic interference that could kill it without, say, setting off a small nuclear bomb?
Yeah, I know how (cosmologically speaking) distance = time, I just meant that they're saying alpha varies in space as well. From the article:
"Along one direction the fine-structure constant, which governs the strength of the electromagnetic force, grows slightly weaker with time, while in the other direction it grows slightly stronger. "
I thought the anomaly described varied in space, rather than time? That is, things further away in one direction had a greater alpha, but ones in the other direction had a lesser alpha.
You'll need a big IR spotlight, though. This wouldn't even need that.
The point being, Moore's Law has had 15 years to work and if someone was selling you a PC from 15 years ago for the same price as it cost 15 years ago, you'd be a bit confused.
"It's 150 Mhz with a WHOLE GIGABYTE of RAM! $1300, with included copy of Windows 98!"
Per wikipedia, it sounds like Anglo-Norman didn't supplant English.
"Although the English language survived and eventually eclipsed Anglo-Norman, the latter had been sufficiently widespread as to permanently affect English lexically. This is why English has lost or, more often, kept as parallel terms many of its original Germanic words which can still be found in German and Dutch. Grammatically, Anglo-Norman had little lasting impact on English, although it is still evident in official and legal terms where the noun and adjective are reversed: attorney general, heir apparent, court martial, body politic, and so on.[2]"
In other words, modern English isn't a descendant of Anglo-Norman.
Old programmers never die, they just hit account block limit.
