Are There More Natural Numbers Than Even Numbers?

Probability Level 3

True or False?

The cardinality (size) of the set of natural numbers 1 , 2 , 3 , … 1,2,3,\ldots is same as the as the cardinality (size) of the set of even numbers − 4 , − 2 , 0 , 2 , 4 , … -4,-2,0,2,4,\ldots .

False True

View wiki
Yash Dev Lamba by Yash Dev Lamba , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Let f : { even numbers } → N f:\{\text{even numbers}\} \rightarrow \mathbb{N} such that f ( 2 n ) = 2 n ,f(0) = 1, f ( − 2 n ) = 2 n + 1 ∀ n ∈ N f(2n) = 2n \text{,f(0) = 1,} f(-2n) = 2n +1 \ \forall n \in \mathbb{N} . This function is a bijective function between both sets, therefore there are as many even numbers as natural numbers

16 Helpful 0 Interesting 0 Brilliant 0 Confused

If natural numbers don't include 0 then it has one less number, if the natural numbers do include 0 then they are the same

Rojo . - 3 years, 2 months ago

Log in to reply

haha, I like your comment... It's true , however, it's not true too, haha

Guillermo Templado - 3 years, 2 months ago

This is true.. but only positive integers are said to be even or odd, not negative integers.

Bhupendra Jangir - 5 years, 4 months ago

Log in to reply

any integer divisible by 2 is an even number irrespective of the sign

bhargav pavuluri - 5 years, 4 months ago

It doesn't matter, both sets defining the even numbers have the same cardinal to set of natural numbers

Guillermo Templado - 5 years, 4 months ago
Phạm Hoàng
Jul 23, 2018

Since there are infinitely natural numbers and even numbers,you can match all natural numbers and even numbers since they are endless.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Jim Cullen
Apr 12, 2018

This is a question that should not have been in the level 3 set theory quiz. It's so much easier than all the other questions here.

First of all, it's trivial knowledge (within the world of set theory) that any set of integers has the same cardinality: aleph zero. But even if you didn't have that knowledge, there's an intuitive sense in which all positive integers have the same "number" of elements as all even integers. Exactly half of all integers.

(Also, 0 is clearly in the set of natural numbers. There's no point in the symbol N if it means the same thing as Z+. But that's not especially relevant.)

1 Helpful 0 Interesting 0 Brilliant 1 Confused

I do not understand. You didn't put in your problem the dots before -4, so in this case the set of even numbers, starting from -4 is obviously lesser than the set of the natural numbers(1,2,3,...).

Oleg Yovanovich

Oleg Yovanovich - 2 years ago

1 pending report

Vote up reports you agree with

×

Problem Loading...

Note Loading...

Set Loading...