# Questions tagged [real-numbers]

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### Are there established complexity classes with real numbers?

A student recently asked me to check an NP-hardness proof for them. They performed a reduction along the lines of: I reduce this problem $P'$ that is known to be NP-complete to my problem $P$ (with ...
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### Representing Negative and Complex Numbers Using Lambda Calculus

Most tutorials on Lambda Calculus provide example where Positive Integers and Booleans can be represented by Functions. What about -1 and i?
Suppose we have a tree in which leaves are labeled with a set of numbers $L$, and internal nodes with a set of operations $O$. In particular $L$ can be $\mathbb{N}, \mathbb{Z}$ or $\mathbb{Q}$, and ...
### What's wrong with this “proof” that $\mathbb{R}$ is enumerable?
The fake proof: We know that $\mathbb{R}$ is uncountable, hence we cannot enumerate over it. But what we do know is that $\mathbb{Q}$, the set of rationals, is countable, and even denumerable. We ...