From what I know: This is still an open question. Here's a list of some approaches. https://mathoverflow.net/questions/310004/categorifications-of-the-real-nu

From what I know: This is still an open question. Here's a list of some approaches. https://mathoverflow.net/questions/310004/categorifications-of-the-real-numbers https://mathoverflow.net/questions/310004/categorifications-...