John Miller reveals the truth about the slandered lemmings.
Several websites do a good job of debunking the myth. Take your pick among snopes.com, the Alaska Department of Fish and Game, the San Francisco Chronicle, etc. Although lemmings migrate due to population pressures and are known to fall from heights and drown in water, they don
Phil Bowermaster is wondering if there’s something dodgy about the math here.
No, this is in fact a standard technique for determining the sum of an infinite series, which is in fact what 0.999… is (it could be expressed as the sum, from n=0 to infinity, of the expression 9 times 10 to the minus n). Perhaps, as one commenter notes, it’s the word “precisely” that’s hanging people up, but certainly that number is equal to one, whatever modifier you want to put on it or leave off.
[Update in the afternoon]
I’m not sure I follow the commenter’s objection. He claims that no matter what you start out with as “a” you get a=1. I don’t see that.
Try it with two, as suggested.
a = 2
10a = 20
10a – a = 20 – 2
9a = 18
Ergo, a = 2.
In fact, do it with 1.999…
a=1.999…
10a = 19.999…
9a = 18
a = 2
As I said, it’s a standard technique for expressing repitends as whole numbers or fractions.
Phil Bowermaster is wondering if there’s something dodgy about the math here.
No, this is in fact a standard technique for determining the sum of an infinite series, which is in fact what 0.999… is (it could be expressed as the sum, from n=0 to infinity, of the expression 9 times 10 to the minus n). Perhaps, as one commenter notes, it’s the word “precisely” that’s hanging people up, but certainly that number is equal to one, whatever modifier you want to put on it or leave off.
[Update in the afternoon]
I’m not sure I follow the commenter’s objection. He claims that no matter what you start out with as “a” you get a=1. I don’t see that.
Try it with two, as suggested.
a = 2
10a = 20
10a – a = 20 – 2
9a = 18
Ergo, a = 2.
In fact, do it with 1.999…
a=1.999…
10a = 19.999…
9a = 18
a = 2
As I said, it’s a standard technique for expressing repitends as whole numbers or fractions.
Phil Bowermaster is wondering if there’s something dodgy about the math here.
No, this is in fact a standard technique for determining the sum of an infinite series, which is in fact what 0.999… is (it could be expressed as the sum, from n=0 to infinity, of the expression 9 times 10 to the minus n). Perhaps, as one commenter notes, it’s the word “precisely” that’s hanging people up, but certainly that number is equal to one, whatever modifier you want to put on it or leave off.
[Update in the afternoon]
I’m not sure I follow the commenter’s objection. He claims that no matter what you start out with as “a” you get a=1. I don’t see that.
Try it with two, as suggested.
a = 2
10a = 20
10a – a = 20 – 2
9a = 18
Ergo, a = 2.
In fact, do it with 1.999…
a=1.999…
10a = 19.999…
9a = 18
a = 2
As I said, it’s a standard technique for expressing repitends as whole numbers or fractions.
Ann Althouse wonders what Neanderthal women did all day.
Maybe they made roast duck. With mango salsa.
Ann Althouse wonders what Neanderthal women did all day.
Maybe they made roast duck. With mango salsa.
Ann Althouse wonders what Neanderthal women did all day.
Maybe they made roast duck. With mango salsa.
This looks like an interesting book–how to think like a rocket scientist.
But pretty cool. Behold, metallic oxygen. It’s red.
And I wouldn’t bet against someone coming up with a use for it. Or something like it:
…high-pressure techniques have already been used to create ultrahard materials such as diamond. Other chemicals, such as nitrogen and carbon monoxide, form solid polymers under pressure that store a lot of energy. If similar structures could be retained at atmospheric pressure, they might make excellent rocket fuel, suggests McMahon.
[Via Geek Press]