Is it hard or proven to be impossible to construct basis $B$ of $\mathbb{R}$ over $\mathbb{Q}$?
Small question regarding the cardinality:(If some miracle happened and CH turned out to be false, then cardinality of $B$ would have the possibility to be strictly between cardinality of natural numbers and real numbers. )I know by Countable/uncountable basis of vector space that it can't have countable basis.