I don't agree with you, or with the sibling comment that claims that "infinity plus one" is "nonsense". It is in fact precisely well-defined, to a mathematician

I don't agree with you, or with the sibling comment that claims that "infinity plus one" is "nonsense". It is in fact precisely well-defined, to a mathematician working in a framework that admits it and makes it worth discussing. The blog post that (I think) started off this chain of posts, at https://blog.plover.com/misc/half-baked.html https://blog.plover.com/misc/half-baked.html , has the most concise and lucid explanation I've found, so I'm just going to straight-up copy it: 0.666...7 is an “an object... said to ‘have order type ω+1’, and is completely legitimate.” It's not very useful – it's exactly equal to 0.666... ! – but it's legitimate and well-defined. My absolute favorite construction of objects like this is Conway's surreal numbers. These things appear perfectly naturally in the surreal numbers, and are completely well-defined, if (again) not very useful.