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Sam Hopkins
Sam Hopkins
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How many different colors do we need so that the set of all possible colorings of R^3$\mathbb{R}^3$ is greater than the powerset of R$\mathbb{R}$. Countably many doesn't seem to be enough and even |R|$|\mathbb{R}|$ seems insufficient. I asked this on stackexchangestackexchange but there is no answer. Is the powerset of R$\mathbb{R}$ the least cardinality of the set of colors for this to hold  ?

How many different colors do we need so that the set of all possible colorings of R^3 is greater than the powerset of R. Countably many doesn't seem to be enough and even |R| seems insufficient. I asked this on stackexchange but there is no answer. Is the powerset of R the least cardinality of the set of colors for this to hold  ?

How many different colors do we need so that the set of all possible colorings of $\mathbb{R}^3$ is greater than the powerset of $\mathbb{R}$. Countably many doesn't seem to be enough and even $|\mathbb{R}|$ seems insufficient. I asked this on stackexchange but there is no answer. Is the powerset of $\mathbb{R}$ the least cardinality of the set of colors for this to hold?

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Arianit
Arianit
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How many colors do we need?

How many different colors do we need so that the set of all possible colorings of R^3 is greater than the powerset of R. Countably many doesn't seem to be enough and even |R| seems insufficient. I asked this on stackexchange but there is no answer. Is the powerset of R the least cardinality of the set of colors for this to hold ?