[Ghoser777]

In a previous thread, someone stated going from 0 to 1 is a 100% increase. That is not the case - it's an infinite percent increase!

Any other pedantic mathematical clarifications that you make?

[dcmacdaddy]

Originally Posted by Ghoser777

In a previous thread, someone stated going from 0 to 1 is a 100% increase. That is not the case - it's an infinite percent increase!

Any other pedantic mathematical clarifications that you make?

Is going from 1 to 2 a 100% increase?

[Dork.]

1/3 is not 33%. Or 33.3%. Or 33.33%. Or 33.333%. and so on.

[The Godfather]

A 1GHz iBook is 25% faster than a 800MHz iBook, but a 800MHz iBook is 20% slower than a 1GHz iBook.

[BlueSky]

One is the loneliest number that you'll ever do. Two can be as bad as one, it's the loneliest number since the number one. I rest my case.

[Ghoser777]

Originally Posted by dcmacdaddy

Is going from 1 to 2 a 100% increase?

Yes. Any time you double your original value you have a 100% increase.

[Dork.]

If you believe Zeno (and his pair of ducks), then you can never leave the room you're currently in, because you'll never make it to the door.

And you thought you'd never need Calculus for anything! Turns out you need it to leave the room!

[ReggieX]

Originally Posted by Dork.

If you believe Zeno (and his pair of ducks), then you can never leave the room you're currently in, because you'll never make it to the door.

That's why Skynyrd were correct in their song:
won’t you give me three steps,
Gimme three steps mister,
Gimme three steps towards the door?
Gimme three steps
Gimme three steps mister,
And you’ll never see me no more.’

Because if you only take 1 or 2 steps, your lim->0 which will halve each time, preventing you from leaving. 3 on the other hand creates the lim->∞ positive feedback loop which will geometrically speed your way out of the room.

[Ghoser777]

Originally Posted by ReggieX

Because if you only take 1 or 2 steps, your lim->0 which will halve each time, preventing you from leaving. 3 on the other hand creates the lim->∞ positive feedback loop which will geometrically speed your way out of the room.

You really lost me here... could you clarify your point a little?

[iomatic]

What do religious people think of these absolutes?

[bewebste]

Originally Posted by BlueSky

One is the loneliest number that you'll ever do. Two can be as bad as one, it's the loneliest number since the number one. I rest my case.

That may be, but three is the magic number.

[f1000]

Originally Posted by Ghoser777

In a previous thread, someone stated going from 0 to 1 is a 100% increase. That is not the case - it's an infinite percent increase!

Any other pedantic mathematical clarifications that you make?

Isn't it an undefined percent increase?

[f1000]

Originally Posted by ReggieX

Because if you only take 1 or 2 steps, your lim->0 which will halve each time, preventing you from leaving. 3 on the other hand creates the lim->∞ positive feedback loop which will geometrically speed your way out of the room.

Sorry, I don't speak gibberish.

[Ghoser777]

Originally Posted by f1000

Isn't it an undefined percent increase?

Pssh, you're just being pedantic.

It's the same situation when you have a vertical line - is the slope infinite or undefined? My google searches seems to indicate that the phrase undefined slope is more commonly used.

[ghporter]

I stick to pedantic things like "it's a Personal Identification NUMBER, so why call it a PIN NUMBER?!?!?!!" (usually acompanied by a strong urge to beat the other person about the head and shoulders). I also do "ATM stands for Automatic Teller Machine, so you're saying you want an Automatic Teller Machine machine? Wouldn't that be what makes ATMs in the first place?" People often give me the same look my dog does when I do that one. Funny!

[tavilach]

There are many infinities of different sizes, such as the infinite amount of numbers between 0 and 1, and the infinite amount of integers from 1 to infinity. The cardinalities of these sets are not equal, so they are different levels of infinity.

[f1000]

Originally Posted by tavilach

There are many infinities of different sizes, such as the infinite amount of numbers between 0 and 1, and the infinite amount of integers from 1 to infinity. The cardinalities of these sets are not equal, so they are different levels of infinity.

It's trivial to show that one can map all the integers greater than 1 into all the real numbers between 0 and 1:

1 = 0.1
2 = 0.01
3 = 0.001
4 = 0.0001
etc.

[f1000]

Originally Posted by Ghoser777

Pssh, you're just being pedantic.

It's the same situation when you have a vertical line - is the slope infinite or undefined? My google searches seems to indicate that the phrase undefined slope is more commonly used.

I'd call the slope of a vertical line undefined.

Did you hear about the recent news on the Twin Prime Conjecture?

[Pendergast]

Originally Posted by tavilach

There are many infinities of different sizes, such as the infinite amount of numbers between 0 and 1, and the infinite amount of integers from 1 to infinity. The cardinalities of these sets are not equal, so they are different levels of infinity.

Yet, some infinities are smaller than others.

The set of Primes versus the Irrationals for instance.

[Daveecee]

n/0 = ∞

[tavilach]

Originally Posted by f1000

It's trivial to show that one can map all the integers greater than 1 into all the real numbers between 0 and 1:

1 = 0.1
2 = 0.01
3 = 0.001
4 = 0.0001
etc.

For cardinalities to be equal, the mappings have to go both ways. Try that. It's not trivial because it's not possible.

[gnomexp]

I also have a lot of fun with numbers to infinite powers... though I'm not sure if it's part of Aleph theory or whatever it's called.

Oh, for pedantical stuff, PLEASE STOP POSTING STATS ALL OVER WITHOUT STANDARD DEVIATIONS AND SAMPLE SIZES! If I have those two numbers, I'll believe any study for what it's worth. Without them, statistics are a steaming pile of poo. "And then there was the man who drowned in a stream with an average depth of 1/2 an inch."

Another biggie is all of the people who don't know how to guestimate the area under the curve using circumscribed and inscribed rectangles. Spending an hour in class on it hurts; I left to heat my lunch and grab a fork and then ate it in class. If they spent that hour on integration with upper and lower bouds, we'd have a much easier time.

[BRussell]

This is more of a probability one than a math one. I think it's related somehow to the Monty Hall problem:

Q: If I flip 2 coins until at least one is a head, what is the probability that the other one is a tail?

A: 2/3, not 1/2 as it might seem.

Or here's one that can make you pause for a second if you're not paying attention:

Q: If we have the same amount of money, and you give me $20, how much more do I have than you?

A: $40.

Or what about this:

Q: If a bottle of wine is worth $10, and the wine alone is worth $9 more than the bottle alone, how much is the bottle worth?

[f1000]

Originally Posted by tavilach

For cardinalities to be equal, the mappings have to go both ways. Try that. It's not trivial because it's not possible.

Well, nothing's trivial to the uninitiated I guess. I've got a better one for you, tav: show us the proof that it's impossible to map the set of reals into the set of integers.

[Ghoser777]

Originally Posted by BRussell

Q: If I flip 2 coins until at least one is a head, what is the probability that the other one is a tail?

A: 2/3, not 1/2 as it might seem.

That question is the same as flipping two coins and noticing that at least one is a head, right? The reason it's 2/3 (which is actually different than the MH problem - much more vexing) is that the possibilities are:

#1 #2
H T
H H
T H

In which case there is a 2 out of 3 chance of the other coin being a tail.

I think your answer to the wine question is $9.50 and $0.50

[Ghoser777]

Originally Posted by f1000

It's trivial to show that one can map all the integers greater than 1 into all the real numbers between 0 and 1:

1 = 0.1
2 = 0.01
3 = 0.001
4 = 0.0001
etc.

That's a one directional mapping - you need a bijection (mapping in both directions) for the cardinalities to be equal.

[Ghoser777]

Originally Posted by f1000

I'd call the slope of a vertical line undefined.

Did you hear about the recent news on the Twin Prime Conjecture?

Are you referring to this?

http://www.post-gazette.com/pg/06034/649668.stm

[iLikebeer]

Originally Posted by Ghoser777

Pssh, you're just being pedantic.

It's the same situation when you have a vertical line - is the slope infinite or undefined? My google searches seems to indicate that the phrase undefined slope is more commonly used.

slope is delta y/delta x, you know, rise over run.
vertical line: infinity/0 => slope=undefined
horizontal line: 0/infinity => slope=0

[f1000]

Originally Posted by BRussell

This is more of a probability one than a math one. I think it's related somehow to the Monty Hall problem:

Q: If I flip 2 coins until at least one is a head, what is the probability that the other one is a tail?

A: 2/3, not 1/2 as it might seem.

Absolutely: HH, HT, TH

That's two out of three outcomes.

Q: If we have the same amount of money, and you give me $20, how much more do I have than you?

A: $40.

(X + $20) - (X - $20) = $40

Q: If a bottle of wine is worth $10, and the wine alone is worth $9 more than the bottle alone, how much is the bottle worth?

W+B=$10
W=B+$9
B+$9+B=$10
2B+$9=$10
B=50 cents

[f1000]

Originally Posted by Ghoser777

That's a one directional mapping - you need a bijection (mapping in both directions) for the cardinalities to be equal.

I didn't mean to imply that their cardinalities were equal. I just assumed that tav knew that the set of reals had a higher cardinality than the set of integers.

Originally Posted by Ghoser777

Are you referring to this?

http://www.post-gazette.com/pg/06034/649668.stm

Yep, that's it.


EDIT: Damn, you beat me to BRussell's problem.

[wataru]

Originally Posted by Daveecee

n/0 = ∞

No. n/0=undefined. The limit of n/x as x goes to 0 = ∞.

[Ghoser777]

Originally Posted by wataru

No. n/0=undefined. The limit of n/x as x goes to 0 = ∞.

You're right. It probably would be better to say that vertical lines have undefined slope... I guess I just have a limit picture in my head when ever I think of a vertical line. I start in my head with the line y=x (slop of 1) and slowly rotate it (increasing slope) until its vertical - the limit of the slopes via that rotation is definitely infinite.

[thunderous_funker]

Its not actually 10". To be honest, its closer to 9.6".

[Daveecee]

Originally Posted by wataru

No. n/0=undefined. The limit of n/x as x goes to 0 = ∞.

Totally what I meant.

[DayLateDon]

Originally Posted by wataru

No. n/0=undefined. The limit of n/x as x goes to 0 = ∞.

That's assuming "n" positive and "x" approaching 0 _from_the_right_, or else "n" negative and "x" approaching 0 _from_the_left_. (Or maybe it's assuming the one-point compactification of the real line --the number loop?-- with an actual point called "infinity" (the reciprocal of 0) that can be approached through positive or negative numbers.) If "n" is non-zero, and if we're dealing with standard analysis, then there is technically no (two-sided) limit. (Finally, for completeness, if "n" is zero, then the limit is zero.)

Likewise ...

Originally Posted by Ghoser777

I start in my head with the line y=x (slop[e] of 1) and slowly rotate it (increasing slope) until it[']s vertical - the limit of the slopes via that rotation is definitely infinite.

More precisely: If you rotate the line counter-clockwise, the slope approaches positive infinity; if you rotate the line clockwise, the slope approaches _negative_ infinity.

I think it's fair and informative --but, note, quite informal-- to describe the limit or the line slope with (the adjective) "infinite". The term captures the qualitative nature of the situation very nicely ... much better than simply saying that the limit "doesn't exist", because there are lots of different ways a limit can fail to exist. Even so, your audience should be made aware that you're using the adjective as shorthand for a situation where "by either approach you take, you hit unboundedly large* numbers".


*"Large" in an absolute-value sense, of course.

Originally Posted by f1000

Sorry, I don't speak gibberish.

Or to put it simply. Pretend you are 10m from the door.

- Before you can walk 10m, you have to walk 5m, leaving you with 5m, left.
- Before you can walk 5m, you have to walk 2.5m, leaving you with 2.5m, left.
- Before you can walk 2.5m, you have to walk 1.25m, leaving you with 1.25m, left.
- Before you can walk 1.25m, you have to walk 0.625m, leaving you with 0.625m, left.
- Before you can walk 0.625m, you have to walk 0.3125m, leaving you with 0.3125m, left.
etc. this goes on forever

Basically, you will always some distance to cover because there will be some distance left to walk, that gets infinitely smaller as you walk more.

[Goldfinger]

Mathematics make my brain hurt

[Eug Wanker]

Originally Posted by The Godfather

A 1GHz iBook is 25% faster than a 800MHz iBook, but a 800MHz iBook is 20% slower than a 1GHz iBook.

Heheh... Many "1 GHz iBooks" are actually 1.07 GHz.

Plus, there are 800 MHz G3 iBooks, whereas all 1 GHz iBooks are G4s. Furthermore, all G4 800 MHz iBooks have 256 KB L2 cache, whereas some 1 GHz iBooks have 512 KB L2 cache.

Is that pedantic enough for you?

[ReggieX]

Originally Posted by f1000

Sorry, I don't speak gibberish.

I think it's perfectly clear for those familiar with Zeno's paradox and Lynyrd Skynyrd lyrics.

[Ghoser777]

Originally Posted by ReggieX

I think it's perfectly clear for those familiar with Zeno's paradox and Lynyrd Skynyrd lyrics.

What I don't get is how three steps "helps."

On my last gas bill it said "You used 20% less gas this year than last year, and it was 10% warmer."

I get the used 20% less part. But what actually is 10% warmer? Where's the baseline temperature? I don't think they were measuring from absolute zero because there's no way the average temperature was 25 degrees higher than last year. It also couldn't be from 0, as 0 degrees is just a measurement along the scale - it's not an actual number of anything physical.

So what does 10% warmer mean?

[ghporter]

Reggie's right; reference to Zeno's paradox shows the subversive and hidden influence of Lynyrd Skynyrd's lyricist, changing perfectly wholesome rock music into something educational...




Hayesk, your utility company is trying to make things "simpler and easier" for their customers. Unfortunately this means that they simplified their numbers too much. Your gas usage baseline is obvious and straightforward. But it would be confusing if they used an historical average temperature for the month, because most customers would need more information. Something like "It was 4% warmer than the historical average temperature for last month," and then post their historical baseline data (more confusion) and so on.

By saying "10% warmer," they may be saying that the average temperature over the past month is numerically 10% higher, or that it was 10% warmer than some historical average, or something else entirely.

[Ghoser777]

Originally Posted by ghporter

By saying "10% warmer," they may be saying that the average temperature over the past month is numerically 10% higher, or that it was 10% warmer than some historical average, or something else entirely.

But how do you measure an increase in temperature? It's not as straightforward as one might think. For example:

30 degrees Celsius + 10% = 33 degrees celsius
86 degrees Fahrenheit (same as 30 celsius) + 10% = 94.6 degrees fahrenheit (really 34.7 degrees celsius)

[ghporter]

Originally Posted by Ghoser777

But how do you measure an increase in temperature? It's not as straightforward as one might think. For example:

30 degrees Celsius + 10% = 33 degrees celsius
86 degrees Fahrenheit (same as 30 celsius) + 10% = 94.6 degrees fahrenheit (really 34.7 degrees celsius)

Precisely. So instead of explaining their reasoning, they just put a number in there and hope nobody will read enough of the bill to wonder about it.

[f1000]

Originally Posted by hayesk

Basically, you will always some distance to cover because there will be some distance left to walk, that gets infinitely smaller as you walk more.

You've just described Zeno's Paradox, but you haven't addressed the innards of Lynyrd Skynyrd's lyrics. See Ghoser's post above for clarification.

[f1000]

Originally Posted by ghporter

Precisely. So instead of explaining their reasoning, they just put a number in there and hope nobody will read enough of the bill to wonder about it.

Sort of like Apple saying that the G4 is twice as fast as the Pentium?