is 0 even or odd?
- Thread starter Drakmeire
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I get a good kick out of reading this thread. People calling one another out with hilarious proofs and "understanding" of math. Failing to realize the difference between a number and an integer, providing fail-proofs, such as defining a number by a function, or using first grader logic as a proof (-1 is odd, 1 is odd, so zero should be as well.) I seriously question the demographic of this site sometimes. I don't see how some of these people graduated high school. Good times. X.x
It's always hilarious how math topics generate so many hits, yet accomplish little to nothing.
"Is Zero a number?"
"Does .99999 (repeating decimal) equal 1?"
Never fails to make me roll my eyes, even just a little.
"Is Zero a number?"
"Does .99999 (repeating decimal) equal 1?"
Never fails to make me roll my eyes, even just a little.
Okay, and you give me the fucking square root of -1. "i" may not be physically definable but it's still a number >.>4li3n said:
Yeesh.
Definition of Even and Odd:
* Even = {2k; ForAll k in Z}
* Odd = {2k+1; ForAll k in Z}
Definition of Z:
* The integers are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...).
0 is Even because:
* 2k[k := 0] is equal to 0.
0 is not Odd because:
* 2k+1[k := (-∞,0):Z] is always negative, and thus not 0.
* 2k+1[k := [0,∞
:Z] is always positive, and thus not 0.
'0' is a number. '0' is not nothing, '0' is an element of Z (Integers), Q (Rational Numbers), R (Reals), C (Complex Numbers) and many more sets. 'Ø' is nothing, the empty set or null set.
Everyone saying that zero isn't a number or isn't even isn't talking about '0', they're talking about 'Ø'. 'Ø' is sometimes, mistakenly, referred to as "zero" in natural language because of the inherent flaws of natural language when it comes to logic (hence the use of formal language).
'Ø' is equal to 0 just as much as the set {A} is equal to 1. 0 is the element count of 'Ø', just like 1 is the element count of {A}.
* Even = {2k; ForAll k in Z}
* Odd = {2k+1; ForAll k in Z}
Definition of Z:
* The integers are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...).
0 is Even because:
* 2k[k := 0] is equal to 0.
0 is not Odd because:
* 2k+1[k := (-∞,0):Z] is always negative, and thus not 0.
* 2k+1[k := [0,∞
:Z] is always positive, and thus not 0.'0' is a number. '0' is not nothing, '0' is an element of Z (Integers), Q (Rational Numbers), R (Reals), C (Complex Numbers) and many more sets. 'Ø' is nothing, the empty set or null set.
Everyone saying that zero isn't a number or isn't even isn't talking about '0', they're talking about 'Ø'. 'Ø' is sometimes, mistakenly, referred to as "zero" in natural language because of the inherent flaws of natural language when it comes to logic (hence the use of formal language).
'Ø' is equal to 0 just as much as the set {A} is equal to 1. 0 is the element count of 'Ø', just like 1 is the element count of {A}.
Precisely my point. (and -1 is me taking an apple away from you, welcome to how these numbers came to be in the first place).PoisonUnagi said:
And infinity exists even if, by it's very definition, you can never get to it... and Achiles never reaches the turtle, it's easily provable.dantoddd said:
Zero is even, by definition of an even number. All Integers are of the for 2n, or 2n+1 which determines if they are odd or even. The concept of splitting something into two groups is a neat way of explaining this, which works for every other Integer, but not zero ( Zero is sometimes your biggest enemy and greatest help in maths. )
Also alot of people seem to think that zero is a concept rather than a number, which is an interesting idea, although not true. Infinity Has this property, and it can rake awhile to get your head around. Using I for infinty the following properties hold.
I+1=I
Lim x = 0
x>I e^x
Lim e^x = I
x>I x
We can see that I doesnt work in regular sums, as infinity will usually make all summations bugger up, however there are different sizes of infinity. Maths be pimping guys
Also alot of people seem to think that zero is a concept rather than a number, which is an interesting idea, although not true. Infinity Has this property, and it can rake awhile to get your head around. Using I for infinty the following properties hold.
I+1=I
Lim x = 0
x>I e^x
Lim e^x = I
x>I x
We can see that I doesnt work in regular sums, as infinity will usually make all summations bugger up, however there are different sizes of infinity. Maths be pimping guys
I am actually a bit confused by your definition as I might be reading it wrong but are you saying that 0 is odd because it is between two odd numbers?Atheist. said:
The problem with infinity is that it can be confused with undefined which is a problem I had when we first did limits. At least that is why I think people have a problem with infinity.4li3n said: