# An intutive explanation of natural density (asymptotic density)

I was wondering if someone can provide an intuitive explanation to natural density. I understand the concept very basically (pretty much the definition) but I can't seem to understand what natural density is and how it, for example, shows that $\frac{1}{2}$ of the integers are odd. I have tried to understand the limit concept that is used through this post but I am having a little difficult visualizing it. If someone could please show a pictorial representation of asymptotic density or explain it in a more visual context then that would be great.

Thanks

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I fixed your post, which reckoned that a third, not a half, was the density of the odd numbers! (: –  Sharkos Apr 27 '13 at 13:35

• A more accurate way Start building two towers, one for odd numbers, one for evens, one block at a time. Take photos every time, zooming out to get everything in the shot (this is the division by $n$ in the limit). Then after a while, the two towers look the same size, because the percentage difference gets smaller and smaller (specifically, given any small number, after a certain time the percentage difference between the heights is as small as you want - the limit part). Alternatively, build one tower with everything in, and one with just odds. Then the second one ends up looking half the height.