There are more even numbers than odd numbers

retina · 2020-08-03, 05:48

Every odd number is half of an even number.

Some even numbers are not double an odd number.

Therefore there are more even numbers than odd numbers.

Nick · 2020-08-03, 08:26

Now you understand why number theorists introduce fractional ideals.

retina · 2020-08-03, 08:51

Quote:

Originally Posted by Nick

Now you understand why number theorists introduce fractional ideals.

https://en.wikipedia.org/wiki/Fractional_ideal

I don't understand?

xilman · 2020-08-03, 09:47

There is precisely one more even number than there are odd numbers.

If a number is odd, so is its negative. All other numbers are even.

However the negative of zero is itself zero. Consequently, it does not have a negative counterpart and is the sole exception mentioned above.

a1call · 2020-08-03, 09:56

I know you are kidding (countable infinities having 1 to 1 relations and all) but I will bite.
For every Even number m.2^n for integers m & n where m is odd, there exists one distinct odd integer m^n sooooo they are equal. I am sure there are other equally invalid logics which will result in there being more odd numbers than even ones but can't think of any just yet.

ETA scrap that that only is distinct off m is not a power.

xilman · 2020-08-03, 10:15

Quote:

Originally Posted by xilman

There is precisely one more even number than there are odd numbers.

If a number is odd, so is its negative. All other numbers are even.

However the negative of zero is itself zero. Consequently, it does not have a negative counterpart and is the sole exception mentioned above.

I apologise. There is an error in statement of the theorem given above.

It should have read "There is precisely one fewer even numbers than there are odd numbers." The proof itself remains unchanged.

a1call · 2020-08-03, 12:54

Quote:

Originally Posted by a1call

I know you are kidding (countable infinities having 1 to 1 relations and all) but I will bite.
For every Even number m.2^n for integers m & n where m is odd, there exists one distinct odd integer m^n sooooo they are equal. I am sure there are other equally invalid logics which will result in there being more odd numbers than even ones but can't think of any just yet.

ETA scrap that that only is distinct off m is not a power.

Let's make another go at this:

For every Even number m^a*2^n for integers m, a & n where m is odd, there exists two distinct odd integer m^n-/+m^a, sooooo there are twice as many odd numbers as there are even ones.

Counterexamples are likely/appreciated.

kriesel · 2020-08-03, 13:50

Quote:

Originally Posted by retina

Some even numbers are not double an odd number.

Do tell. Give a list of five of them that are not immediately preceded by an odd number each.

retina · 2020-08-03, 13:55

Quote:

Originally Posted by kriesel

Do tell. Give a list of five of them that are not immediately preceded by an odd number each.

4, 8, 16 ,32, 64

JeppeSN · 2020-08-04, 01:06

I do see some correct statements above. They should be moved out of this crackpot subforum, by someone. Am I being trolled? /JeppeSN

storm5510 · 2020-08-04, 14:20

All of this seems to make something very simple into something very complex. It is not. If you take them in pairs, (one of each type), the count will be the same for odds and evens, if the counting stops on an even.

(1,2)(3,4)(5,6)(7,8) and so on.

2020-08-03, 05:48	#1
retina Undefined "The unspeakable one" Jun 2006 My evil lair 2×3⁴×37 Posts	There are more even numbers than odd numbers Every odd number is half of an even number. Some even numbers are not double an odd number. Therefore there are more even numbers than odd numbers.

2020-08-03, 09:56	#5
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 7×283 Posts	I know you are kidding (countable infinities having 1 to 1 relations and all) but I will bite. For every Even number m.2^n for integers m & n where m is odd, there exists one distinct odd integer m^n sooooo they are equal. I am sure there are other equally invalid logics which will result in there being more odd numbers than even ones but can't think of any just yet. ETA scrap that that only is distinct off m is not a power. Last fiddled with by a1call on 2020-08-03 at 10:01

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2020-08-03, 08:26	#2
Nick Dec 2012 The Netherlands 1582₁₀ Posts	Now you understand why number theorists introduce fractional ideals.

2020-08-03, 09:47	#4
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 10,499 Posts	There is precisely one more even number than there are odd numbers. If a number is odd, so is its negative. All other numbers are even. However the negative of zero is itself zero. Consequently, it does not have a negative counterpart and is the sole exception mentioned above.

2020-08-04, 01:06	#10
JeppeSN "Jeppe" Jan 2016 Denmark 163 Posts	I do see some correct statements above. They should be moved out of this crackpot subforum, by someone. Am I being trolled? /JeppeSN

2020-08-04, 14:20	#11
storm5510 Random Account Aug 2009 U.S.A. 3²×199 Posts	All of this seems to make something very simple into something very complex. It is not. If you take them in pairs, (one of each type), the count will be the same for odds and evens, if the counting stops on an even. (1,2)(3,4)(5,6)(7,8) and so on.