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        riddles >> general problem-solving / chatting / whatever >> Silly question *new question at bottom*
        
(Message started by: Hooie on May 26th, 2004, 9:47pm)
Title: Silly question *new question at bottom*
Post by Hooie on May 26th, 2004, 9:47pm
Is infinity even or odd? Or does it not apply to infinity?
Title: Re: Silly question
Post by Sphere on May 26th, 2004, 10:59pm
if infinity is even, is infinity + 1 odd ?

actually infinity + 1 is again infinity...in fact infinity is not a countable number or integer or something you can divide by 2 and get a result

it is neither even nor odd...
Title: Re: Silly question
Post by THUDandBLUNDER on May 26th, 2004, 11:30pm
Is zero odd or even?
Title: Re: Silly question
Post by towr on May 26th, 2004, 11:36pm
I'd say even, it's in between two odd numbers after all
Of course as numbers go it's pretty odd as well. In that light infinity is a very odd number  ;D
Title: Re: Silly question
Post by rmsgrey on May 27th, 2004, 2:31am
Is infinity divisible by 2? The result is certainly not an integer since all integers are finite...

Of course, you also have to decide whether "even numbers" are defined as those divisible by two, or by some other equivalent (among finite numbers) property.

I suspect the answer is either "whichever is consistent with your axioms" or "pick one".
Title: Re: Silly question
Post by Hooie on May 27th, 2004, 6:50pm
TB, isn't zero even? It's divisble by 2.
Title: Re: Silly question
Post by Icarus on May 27th, 2004, 8:04pm
0 is even (and not odd). [infty] and [smiley=varaleph.gif]0 are neither - the concept really doesn't extend to these infinities. [omega] could be considered even, but this time the concept is not particularly useful, so why bother?
Title: Re: Silly question
Post by Eigenray on May 27th, 2004, 11:24pm

on 05/27/04 at 20:04:18, Icarus wrote:
[omega] could be considered even, but this time the concept is not particularly useful, so why bother?

It seems most natural to call x even if there exisys y such that x = y+y = y2.
Then, if I'm doing this right, [omega]n + k is even iff n is even, where k,n are finite, n>0.  So [omega] would be odd.  This is because ([omega]n+k)+([omega]n+k) = ([omega]n+k)2 = [omega]2n + k.

Or, we can call x even if there exists y such that x = 2y.
Then [omega]n + k is even iff k is even, I think, and [omega] would be even.  This is because 2([omega]n+k) = [omega]n+2k.

I guess it comes down to whether even means "can be divided into two equal parts" (y2) or "can be split into pairs" (2y).  For finite ordinals, of course, both are the same.
Title: Re: Silly question
Post by grimbal on May 28th, 2004, 12:21pm
Is [pi] even or odd?
Title: Re: Silly question
Post by Three Hands on May 28th, 2004, 1:24pm
Given it doesn't divide by two, I'd say it isn't even. I know it's irrational, but beyond that, I'm not sure - don't do enough maths ::)
Title: Re: Silly question
Post by Icarus on May 28th, 2004, 6:09pm
Yet another example of numbers to which "Even" & "Odd" do not extend in a useful manner. Applying either of Eigenray's definitions to the set of Real numbers leaves you with the result that all real numbers are "even" - including the odd integers. Since this is useless, we don't make such a definition, so [pi] is neither even or odd.

Eigenray - I hadn't considered that left and right multiplication by 2 would give you differing definitions of "Even". So in the ordinals, we actually have 4 designations: "Left-even" vs "Left-odd", and "Right-even" vs "Right-odd".

Which strikes me as being downright odd!  ::)

Thanks for pointing that out.
Title: Re: Silly question *new question at bottom*
Post by Hooie on Jun 1st, 2004, 10:22pm
Okay, I have another question. I'm adding it here instead of making another thread.

What do you get when you integrate a position function? Does it have any meaning in real life? I can't imagine how position would be a rate of change of something else with respect to time.

:) Let me know when my silly questions get annoying.
Title: Re: Silly question *new question at bottom*
Post by towr on Jun 2nd, 2004, 4:33am
You could use it to find the average position (weighed with time).
[int]x(t) dt ]/t
Must be good for something.
Title: Re: Silly question
Post by otter on Jun 16th, 2004, 1:39pm

on 05/26/04 at 23:30:18, THUDandBLUNDER wrote:
Is zero odd or even?

As an aside, why is zero so often used with the plural form of objects (at least in English)?  For example, "After removing the last one, there were zero balls left in the box."  Certainly would sound strange to answer "There is zero ball."  I'm sure it's just a grammatical construction, but it struck a chord.  Go figure...
Title: Re: Silly question
Post by Grimbal on Jun 16th, 2004, 3:47pm

on 06/16/04 at 13:39:51, otter wrote:
As an aside, why is zero so often used with the plural form of objects (at least in English)?  For example, "After removing the last one, there were zero balls left in the box."  Certainly would sound strange to answer "There is zero ball."  I'm sure it's just a grammatical construction, but it struck a chord.  Go figure...


Simple.  The singular is for one.  Zero is not one.  So you don't use the singular.

It would be logical to use the genitive form for zero.  I.e. zero of ball.

It reminds me of the joke:
- What did you do for holidays?
- I went to Canada, fishing salmon.
- Wow, did you catch any?
- Actually, no.
- So how do you know it is salmon you were fishing?

From this, you should say I have zero.  Because if you have zero ball(s) or zero umbrella(s), the result is the same, isn't it?

Another question: is it 1.5 ball or 1.5 balls?

And is it 1.99999... ball or 1.99999... balls?  ;D

Sorry, a lots of thoughts in one post.
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Jun 17th, 2004, 12:43pm
Salmon is both singular and plural, so probably not a good example. If I said I was hunting lions, then the plural form would be used throughout the joke.

I would automatically say 1.5 balls and similarly for 1.999.... balls. The real question there is what's correct for 0.9999... ball(s)?

The other issue that often confuses people is "less" and "fewer". Assuming that all sheep are equal and there is only one type of water, which of the following are (grammatically) correct?

a)I have less sheep than a shepherd
b)I have fewer sheep than a shepherd
c)The tap has less water than the ocean
d)The tap has fewer waters than the ocean
Title: Re: Silly question *new question at bottom*
Post by Three Hands on Jun 17th, 2004, 4:55pm
I believe the answers you are looking for are [hide]b and c[/hide]

Boy, will I look stupid if I've managed to get that wrong, especially seeing as it's one of rmsgrey's pet peeves... ::)
Title: Re: Silly question *new question at bottom*
Post by towr on Jun 18th, 2004, 12:44am
I'd say they're all syntactically possible, but b,c are semantically plausable.
But f.i. if I slaughter a sheep (and cook it up for good measure) and give you a leg, and take the rest for myself, then you have less sheep than I have :P (though I suppose when cooked it's more proper to refer to it as mutton)
And even if there is only one kind of water, it is not a logical contradiction for there to have been more kinds, and so it's grammatical to talk about those hypothetical kinds.
The supermarkets around here sell all kinds of waters, evian, sourcy, bar-le-duc etc. The tap has significantly fewer waters..
Title: Re: Silly question *new question at bottom*
Post by Grimbal on Jun 18th, 2004, 6:04am

on 06/17/04 at 12:43:40, rmsgrey wrote:
Salmon is both singular and plural, so probably not a good example. If I said I was hunting lions, then the plural form would be used throughout the joke.

What I meant is that if didn't caught any, you were not hunging lion(s), you were just hunting.


on 06/17/04 at 12:43:40, rmsgrey wrote:
I would automatically say 1.5 balls and similarly for 1.999.... balls. The real question there is what's correct for 0.9999... ball(s)?

When I see 1.5, I think one and a half.  So 1.5 ball sounds just as good to me.

Anyway, I would say the singular/plural is really defined for integers.  For anything else, reals, fractions, or unknowns (n balls), I take the liberty to do as I feel.  Even though established gramaticians might feel otherwise.
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Jun 19th, 2004, 5:43am
Three Hands was right, but as Towr pointed out, the other two are not syntactically wrong, just have different meanings from the ones you might expect - which is why it matters which you use: not because of arbitrary rules, but because the meaning is different, so confusing the two leads to ambiguities in some cases.

As to fishing for zero salmon, my angling acquaintance informs me that the techniques and equipment you use for fishing varies (if you're what they regard as serious) depending on what sort of fish you're going for. So you can be specifically fishing for salmon even when you fail to catch anything (After all, you also fail to shoot down any waterfowl, but it would be unusual to ask how you know that you were fishing for salmon rather than shooting ducks).

There are, of course, other situations when just saying "zero" without some sort of units to qualify is clearly wrong. For instance, in talking about temperature, were I to say that it's zero degrees, you could be justifiably confused as to whether mildly impure water would be solid, and also whether air would be gaseous.
Title: Re: Silly question *new question at bottom*
Post by towr on Jun 20th, 2004, 7:32am

on 06/19/04 at 05:43:05, rmsgrey wrote:
For instance, in talking about temperature, were I to say that it's zero degrees, you could be justifiably confused as to whether mildly impure water would be solid, and also whether air would be gaseous.
Not whether air would be gaseous, as absolute 0 is 0 kelvin, not 0 degrees kelvin. But it's still up in the air wether it's degrees Fahrenheit or degrees Celsius/centigrade..
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Jun 21st, 2004, 8:18am
I'm sure I've heard people talking about "0 degrees absolute"
Title: Re: Silly question *new question at bottom*
Post by towr on Jun 21st, 2004, 10:12am
I'm sure you have. Unfortunately a lot of people don't know what they're saying, nor what they're talking about, and so can't be trusted in that regard..

I suppose it doesn't help that a difference of one degree centigrade is equal to a difference of one kelvin. So it's easy to combine those to 'x degrees above absolute 0', however that makes it 'x kelvin', not 'x degrees <kelvin,centigrade,fahrenheit or other>'.
Title: Re: Silly question *new question at bottom*
Post by Eigenray on Jun 21st, 2004, 11:00am
In school they told us it was "x Kelvin" when talking about an actual temperature, but "x degrees (Kelvin)" when talking about a temperature difference.

It made sense at the time ... same as the difference between "2 o'clock" and "2 hours".
Title: Re: Silly question *new question at bottom*
Post by towr on Jun 21st, 2004, 11:28am
Always be suspicious of teachers..
If you talk about a diffence in temperatures you can use degrees, but that would make it degrees (Celsius), the Kelvin scale has kelvins, K, as units, de Celcius scale has degrees centigrade, oC. Just like time has seconds, s, as units, and not degrees (time) :P

Besides, it's only proper to use the SI units when dealing with science.
Title: Re: Silly question *new question at bottom*
Post by Icarus on Aug 2nd, 2004, 8:22pm
From the better-late-than-never department:


on 06/21/04 at 08:18:54, rmsgrey wrote:
I'm sure I've heard people talking about "0 degrees absolute"


Is this from the same guy who was complaining about people saying such things as "less sheep" when they meant "fewer"? This is no better.


on 06/21/04 at 11:00:16, Eigenray wrote:
In school they told us it was "x Kelvin" when talking about an actual temperature, but "x degrees (Kelvin)" when talking about a temperature difference.

It made sense at the time ... same as the difference between "2 o'clock" and "2 hours".


It isn't what I was taught, nor does it make sense to me. I was taught "x Kelvins" for both, just as you would say "x grams", not "x degrees gram". Degrees Celsius or Degrees Farenheit are called such because they represent an arbitrary scale placed on the range of temperature. Kelvins, however, represent a unit of temperature, and the expression of temperature by Kelvins is just a statement of how many of these units are present. Thus saying "278 Kelvin" is no more grammatical than saying "278 gram". It should be "278 Kelvins", and never "278 degrees Kelvin", no matter whether expressed as an absolute temperature or a temperature difference.


on 06/21/04 at 11:28:00, towr wrote:
Besides, it's only proper to use the SI units when dealing with science.


Nay! CGS is clearly the only system for science! No upstart like SI will ever replace it!
Title: Re: Silly question *new question at bottom*
Post by towr on Aug 3rd, 2004, 1:20am
CGS? Can't say I ever heard of it..
Besides SI just standa for international system of units. Regardless of what exactly it is, an international standard is certainly better than having scientists working together at some international project using different standards and letting their spacecraft crash into mars because they can't tell their feet from their meters..
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Aug 3rd, 2004, 5:20am
centimeter gramme second...

OK, maybe I should have said "people I would expect to know [better] talking about 0 degrees absolute"
Title: Re: Silly question *new question at bottom*
Post by Grimbal on Aug 3rd, 2004, 8:34am
I learned something new.  I always thought the unit was the degree, and there were 3 of them, the degree Celsius °C, the degree Fahrenheit °F and the degree Kelvin °K.  But it seems some comitee decided the kelvin *is* the unit.  Now we all have to comply.

See http://en.wikipedia.org/wiki/Kelvin

But about the symbol, they first say "The kelvin as an SI unit is correctly written with a lowercase k (unless at the beginning of a sentence), and is never preceded by the words degree or degrees, or the symbol °, [...]", then they say "Note that the symbol for the kelvin unit is always a capital K and never italicised."

???
Title: Re: Silly question *new question at bottom*
Post by Icarus on Aug 19th, 2004, 8:13pm
Resistance is futile. You will be assimilated...

Actually, there is a 4th measure of temperature, but I have never seen anyone actually use it. The "renkin" (if I recall the name correctly) is, like the kelvin, an absolute unit of temperature, but its size is the same as a degree Farenheit, rather than a degree Celsius.

As for the capitalization bit, what they are saying is that the unit is named "kelvin", not "Kelvin", but is symbolized by "K", not "k". This actually matches the conventions for most units of measure named after people.
Title: Re: Silly question *new question at bottom*
Post by EZ_Lonny on Aug 25th, 2004, 5:10am
Why do we speak of "degrees" Celsius and Fahrenheit and not of "degrees" Kelvin ?
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Aug 25th, 2004, 5:40am
Short answer: Because a committee said so.
Title: Re: Silly question *new question at bottom*
Post by EZ_Lonny on Aug 26th, 2004, 4:45am
What committee? And why did they say so?

I think it has to do with Kelvin himself. He's said: "There's only one Kelvin and not any degree of me. Let Celsius and Fahrenheit have them"  >:(
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Aug 26th, 2004, 5:36am
The General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures).

According to this (http://physics.nist.gov/cuu/Units/kelvin.html) site:

Quote:
The definition of the unit of thermodynamic temperature was given in substance by the 10th CGPM (1954) which selected the triple point of water as the fundamental fixed point and assigned to it the temperature 273.16 K, so defining the unit. The 13th CGPM (1967) adopted the name kelvin (symbol K) instead of "degree Kelvin" (symbol °K) and defined the unit of thermodynamic temperature


So it possibly used to be the degree Kelvin until 1967, when the degree was dropped.

[e]prettify link[/e]
Title: Re: Silly question *new question at bottom*
Post by towr on Aug 26th, 2004, 5:46am
It's a bit like asking "why aren't there degrees radian"
In angles a degree is a part (1/360th or sometimes 1/400th) of a whole circle. And in temperature a degree is a part of some (fairly arbitrary) scale (either Celsius' or Fahrenheits).
A kelvin on the other hand is not a subdivision of some fixed length scale (like f.i. freezing point to boiling point, or like in the case of a circle one circumference).
Arguably the celsius scale could have been different at different altitudes, because boiling/freezing point of water changes with pressure. Just like for speed 'mach 1' is different at different altitudes, because the speed of sound differs.
Luckily people were a bit more sensible than to put up with something like that in the case of temperature..
Title: Re: Silly question *new question at bottom*
Post by Sir Col on Aug 31st, 2004, 4:55am
I have some "silly" questions...

(1) What happens to the boiling point of other liquids at different pressures? Do they all change by the same proportion?

(2) I know that the point at which vapour pressure is equal to atmospheric pressure defines the boiling point of a liquid, but what happens in a vacuum? What temperature would water boil/freeze at?

(3) Perhaps this is bordering the philosophical, but is H2O still water when it is solid/gaseous? In other words, is water the name given exclusively to the liquid form?

[e]Edited italics; for some reason I originally wrote temperatures?[/e]
Title: Re: Silly question *new question at bottom*
Post by rmsgrey on Aug 31st, 2004, 6:07am
1) Dunno

2) Below a certain pressure, water sublimes - passes directly from solid to vapour without passing through a liquid state. Carbon Dioxide (dry ice) does this at atmospheric pressure. Not sure what Helium does.

3) "Water" has two distinct meanings, which are usually not distinguished - on the one hand, it is the common name for H2O in its liquid phase with not more than a reasonable level of dissolved impurities present (consider what passes for water in various rivers); on the other, it is the formal name for the chemical H2O regardless of phase, but with an assumed no impurities.
Title: Re: Silly question *new question at bottom*
Post by Icarus on Sep 17th, 2004, 8:03pm
(1) Other materials than water also change their boiling points and freezing points in response to atmospheric pressure. I do not believe the change is of the same proportion. It depends on many things.

(2) (In response to rmsgrey): Helium does not exist in solid form, except perhaps at very high pressures, so it does not sublimate in a vacuum!

Liquids in a vacuum, if they retain their liquid state, still evaporate as before, just at a higher rate.


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