3 ms·
> ω+1 = ω+1 , i.e. "the next thing after infinity" I find this concept perplexing. To me this implies that "infinity" has a value. How can you add 1 to a thing
by squidsoup 3y ago
> ω+1 = ω+1 , i.e. "the next thing after infinity"
I find this concept perplexing. To me this implies that "infinity" has a value. How can you add 1 to a thing that by definition has no value?
- gus_massa 3y agoSymbols in math are overloaded, like in C++. Imagine the + in C++ when you have to add two complex numbers. They are just a struct with x and y, and some magic to make all operations work as intended. The use of the + in this example is more like the concatenation of strings, like "Hello " + "World!" is "Hello World!". But in this case, the content of the string doesn't matter so "Hello " == "World!" and there are some magical strings that are infinite. The idea is that anyone can overload the symbol + and sum whatever they want. It's not necessary to use + with numbers. Obviously, most silly overloads are ignored, and nobody use them. In this case it's a popular overload so it is teach in an advanced math course and has it's own Wikipedia article.
- squidsoup 3y agoThanks for the explanation, that was helpful.