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> **Possible Duplicate:**  
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> [Is there a known well ordering of the reals?](https://math.stackexchange.com/questions/6501/is-there-a-known-well-ordering-of-the-reals) 
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I am having a hard time wrapping my head around what a well-ordering of $\mathbb{R}$ looks like. I have seen the presentation of a well-ordering of $\mathbb{Z}$ ie $0, -1, 1, -2, 2, \ldots$ but how could you do this type of ordering with $\mathbb{R}$ where numbers are not countable in that way?

Edit: I'm guessing what I'm asking is if $0, -\epsilon , \epsilon, -2\epsilon, 2\epsilon,\ldots$ could be thought of as a well-ordering of $\mathbb{R}$ in a similar fashion.