Author |
Topic: Silly question *new question at bottom* (Read 1571 times) |
|
Hooie
Newbie
Gender: 
Posts: 29
|
 |
Silly question *new question at bottom*
« on: May 26th, 2004, 9:47pm » |
 Quote  Modify
|
Is infinity even or odd? Or does it not apply to infinity?
|
| « Last Edit: Jun 1st, 2004, 10:20pm by Hooie » |
 IP Logged |
|
|
|
Sphere
Newbie
Posts: 1
|
|
Re: Silly question
« Reply #1 on: May 26th, 2004, 10:59pm » |
Quote Modify
|
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...
|
|
IP Logged |
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Silly question
« Reply #2 on: May 26th, 2004, 11:30pm » |
Quote Modify
|
Is zero odd or even?
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question
« Reply #3 on: May 26th, 2004, 11:36pm » |
Quote Modify
|
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 
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
rmsgrey
Uberpuzzler
    
Gender:
Posts: 2873
|
|
Re: Silly question
« Reply #4 on: May 27th, 2004, 2:31am » |
Quote Modify
|
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".
|
|
IP Logged |
|
|
|
Hooie
Newbie
Gender:
Posts: 29
|
|
Re: Silly question
« Reply #5 on: May 27th, 2004, 6:50pm » |
Quote Modify
|
TB, isn't zero even? It's divisble by 2.
|
|
IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Silly question
« Reply #6 on: May 27th, 2004, 8:04pm » |
Quote Modify
|
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?
|
| « Last Edit: May 27th, 2004, 8:05pm by Icarus » |
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
|
Re: Silly question
« Reply #7 on: May 27th, 2004, 11:24pm » |
Quote Modify
|
on May 27th, 2004, 8:04pm, 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.
|
|
IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Silly question
« Reply #8 on: May 28th, 2004, 12:21pm » |
Quote Modify
|
Is [pi] even or odd?
|
|
IP Logged |
|
|
|
Three Hands
Uberpuzzler
Gender:
Posts: 715
|
|
Re: Silly question
« Reply #9 on: May 28th, 2004, 1:24pm » |
Quote Modify
|
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 
|
|
IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Silly question
« Reply #10 on: May 28th, 2004, 6:09pm » |
Quote Modify
|
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.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Hooie
Newbie
Gender:
Posts: 29
|
|
Re: Silly question *new question at bottom*
« Reply #11 on: Jun 1st, 2004, 10:22pm » |
Quote Modify
|
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.
|
| « Last Edit: Jun 1st, 2004, 10:23pm by Hooie » |
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question *new question at bottom*
« Reply #12 on: Jun 2nd, 2004, 4:33am » |
Quote Modify
|
You could use it to find the average position (weighed with time).
[[int]x(t) dt ]/t
Must be good for something.
|
| « Last Edit: Jun 2nd, 2004, 4:44am by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
otter
Junior Member
Gender:
Posts: 142
|
|
Re: Silly question
« Reply #13 on: Jun 16th, 2004, 1:39pm » |
Quote Modify
|
on May 26th, 2004, 11:30pm, THUDandBLUNDER 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...
|
| « Last Edit: Jun 16th, 2004, 1:40pm by otter » |
IP Logged |
We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
T.S. Eliot
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Silly question
« Reply #14 on: Jun 16th, 2004, 3:47pm » |
Quote Modify
|
on Jun 16th, 2004, 1:39pm, 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?
Sorry, a lots of thoughts in one post.
|
|
IP Logged |
|
|
|
rmsgrey
Uberpuzzler
Gender:
Posts: 2873
|
|
Re: Silly question *new question at bottom*
« Reply #15 on: Jun 17th, 2004, 12:43pm » |
Quote Modify
|
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
|
|
IP Logged |
|
|
|
Three Hands
Uberpuzzler
Gender:
Posts: 715
|
|
Re: Silly question *new question at bottom*
« Reply #16 on: Jun 17th, 2004, 4:55pm » |
Quote Modify
|
I believe the answers you are looking for are b and c
Boy, will I look stupid if I've managed to get that wrong, especially seeing as it's one of rmsgrey's pet peeves...
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question *new question at bottom*
« Reply #17 on: Jun 18th, 2004, 12:44am » |
Quote Modify
|
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  (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..
|
| « Last Edit: Jun 18th, 2004, 12:47am by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Silly question *new question at bottom*
« Reply #18 on: Jun 18th, 2004, 6:04am » |
Quote Modify
|
on Jun 17th, 2004, 12:43pm, 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 Jun 17th, 2004, 12:43pm, 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.
|
|
IP Logged |
|
|
|
rmsgrey
Uberpuzzler
Gender:
Posts: 2873
|
|
Re: Silly question *new question at bottom*
« Reply #19 on: Jun 19th, 2004, 5:43am » |
Quote Modify
|
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.
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question *new question at bottom*
« Reply #20 on: Jun 20th, 2004, 7:32am » |
Quote Modify
|
on Jun 19th, 2004, 5:43am, 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..
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
rmsgrey
Uberpuzzler
Gender:
Posts: 2873
|
|
Re: Silly question *new question at bottom*
« Reply #21 on: Jun 21st, 2004, 8:18am » |
Quote Modify
|
I'm sure I've heard people talking about "0 degrees absolute"
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question *new question at bottom*
« Reply #22 on: Jun 21st, 2004, 10:12am » |
Quote Modify
|
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>'.
|
| « Last Edit: Jun 21st, 2004, 10:14am by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
|
Re: Silly question *new question at bottom*
« Reply #23 on: Jun 21st, 2004, 11:00am » |
Quote Modify
|
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".
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Silly question *new question at bottom*
« Reply #24 on: Jun 21st, 2004, 11:28am » |
Quote Modify
|
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)
Besides, it's only proper to use the SI units when dealing with science.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print