Is zero an even number?
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1 + ∞ != ∞ :)
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Only people who cannot count would consider zero as anything other than even. It is the most even of all the even numbers, and there are so many ways of describing it as even that it is pointless to try. It is also the reason why the number of even numbers is bigger than the number of odd numbers, and yet they are both infinite.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
Ah yes, ad hominem attacks, the proof of accountants! ;)
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Sure, but does adding or subtracting 1 make a small infinity large or a large small, respectively? Douglas Hofstadter has quite a nice basic intro to differences between infinities in Gödel, Escher, Bach.[^]
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1 + ∞ != ∞ :)
That's what you get when you mix set cardinality with count.
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Sure, but does adding or subtracting 1 make a small infinity large or a large small, respectively? Douglas Hofstadter has quite a nice basic intro to differences between infinities in Gödel, Escher, Bach.[^]
The difference is always in the definition. Like the Infinite Hotel Paradox or the differences between the sets of a Natural Number Infinity and a Real Number Infinity. In both cases one of the infinities is larger than the other. In the first it is Exactly Double the size, and in the seconds it is Infinitely Bigger. Similarly, the difference between the Set Of Natural Numbers that are odd and the Set of Natural Numbers that are even is one, even though both of them are infinitely large.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
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The difference is always in the definition. Like the Infinite Hotel Paradox or the differences between the sets of a Natural Number Infinity and a Real Number Infinity. In both cases one of the infinities is larger than the other. In the first it is Exactly Double the size, and in the seconds it is Infinitely Bigger. Similarly, the difference between the Set Of Natural Numbers that are odd and the Set of Natural Numbers that are even is one, even though both of them are infinitely large.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
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Only people who cannot count would consider zero as anything other than even. It is the most even of all the even numbers, and there are so many ways of describing it as even that it is pointless to try. It is also the reason why the number of even numbers is bigger than the number of odd numbers, and yet they are both infinite.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
Dalek Dave wrote:
It is also the reason why the number of even numbers is bigger than the number of odd numbers, and yet they are both infinite.
In what sense? The sets of odd and even numbers have the same cardinality and asymptotic density.
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Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.
A fun bit of silliness for Monday morning. BTW, the answer is yes.
Panic, Chaos, Destruction. My work here is done. Drink. Get drunk. Fall over - P O'H OK, I will win to day or my name isn't Ethel Crudacre! - DD Ethel Crudacre I cannot live by bread alone. Bacon and ketchup are needed as well. - Trollslayer Have a bit more patience with newbies. Of course some of them act dumb - they're often *students*, for heaven's sake - Terry Pratchett
Quote:
This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. ref Even_number
0/2 = 0 but 0.0/2 = 0.0 and if 0 is a number then '.0' is a remainder thus 0 is an odd number :P
First BASIC, then q-BASIC, moved to Pascal and Delphi, studied and work on C++, moved to C# and (unfortunately VB), learned JavaScript and after all these languages learned... when I travel abroad I have to speak English. browse-offline.com
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Quote:
This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. ref Even_number
0/2 = 0 but 0.0/2 = 0.0 and if 0 is a number then '.0' is a remainder thus 0 is an odd number :P
First BASIC, then q-BASIC, moved to Pascal and Delphi, studied and work on C++, moved to C# and (unfortunately VB), learned JavaScript and after all these languages learned... when I travel abroad I have to speak English. browse-offline.com
Not a real example, it is non-calculable. The mathematical term is 'Indeterminate' Here is another paradox... X/∞ = 0 Therefore X = ∞ . 0 But then X would be the same for any value of X, and that is plainly wrong.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
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Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.
A fun bit of silliness for Monday morning. BTW, the answer is yes.
Panic, Chaos, Destruction. My work here is done. Drink. Get drunk. Fall over - P O'H OK, I will win to day or my name isn't Ethel Crudacre! - DD Ethel Crudacre I cannot live by bread alone. Bacon and ketchup are needed as well. - Trollslayer Have a bit more patience with newbies. Of course some of them act dumb - they're often *students*, for heaven's sake - Terry Pratchett
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Only people who cannot count would consider zero as anything other than even. It is the most even of all the even numbers, and there are so many ways of describing it as even that it is pointless to try. It is also the reason why the number of even numbers is bigger than the number of odd numbers, and yet they are both infinite.
--------------------------------- I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave CCC Link[^]
Dalek Dave wrote:
the number of even numbers is bigger than the number of odd numbers, and yet they are both infinite.
That's one of my favorites to bring up to non-math people.... You can tell that their brain hurts... :laugh:
The United States invariably does the right thing, after having exhausted every other alternative. -Winston Churchill America is the only country that went from barbarism to decadence without civilization in between. -Oscar Wilde Wow, even the French showed a little more spine than that before they got their sh*t pushed in.[^] -Colin Mullikin
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I know. I find it pretty odd as well...
The United States invariably does the right thing, after having exhausted every other alternative. -Winston Churchill America is the only country that went from barbarism to decadence without civilization in between. -Oscar Wilde Wow, even the French showed a little more spine than that before they got their sh*t pushed in.[^] -Colin Mullikin
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I know. I find it pretty odd as well...
The United States invariably does the right thing, after having exhausted every other alternative. -Winston Churchill America is the only country that went from barbarism to decadence without civilization in between. -Oscar Wilde Wow, even the French showed a little more spine than that before they got their sh*t pushed in.[^] -Colin Mullikin
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:thumbsup: :laugh:
The United States invariably does the right thing, after having exhausted every other alternative. -Winston Churchill America is the only country that went from barbarism to decadence without civilization in between. -Oscar Wilde Wow, even the French showed a little more spine than that before they got their sh*t pushed in.[^] -Colin Mullikin
