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Is there a known well ordering of the reals?
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.