A repeating sequence can be generated by a computer program. There are only countably many computer programs, so there are only countably many repeating sequences.
That's an interesting point. A computer program is itself a finite number of symbols chosen from a finite list (with certain restrictions that further reduce the number of programs that make sense).
The same can be said for the English language. In fact, the same can be said for any language that can be translated into English, or into any other language that has a finite alphabet.
And I don't know how a language with an infinite alphabet would work, but if it can be explained in English, then that implies that it can be translated to English.
This therefore implies that there must exist numbers which cannot be precisely specified at all.
there must exist numbers which cannot be precisely specified at all.
Almost all of them! But, y'know, I can't tell you what any of them are :-).
Edit: I didn't realize this before writing the post, but what I'm referring to is The Principle of Charity.
Story
I was confused about Node Modules, so I did a bunch of research to figure out how they work. Explaining things helps me to understand them, and I figured that others might benefit from my explanation, so I wrote a blog post about them. However, I'm inexperienced and still unsure of exactly what's going on, so I started the blog post off with a disclaimer:
My friend said that it's a bad idea to do that. He said:
I interpreted what he said literally and basically responded by saying:
This was stupid of me. He didn't mean "claim that you're 100% sure of what you've written". He didn't mean "pretend that you're way more confident in what you've written than what you really are". He meant, "I think that it comes across as you being less confident than you actually are. And so I think you should reword it to better communicate your confidence."
I shouldn't have interpreted what he said so literally. I should have thought about and responded to what I thought he meant to say. (Although, he also should have been more precise...)
Thesis
People often interpret and respond to statements literally. Instead of doing this, it's often useful to think about and respond to what the other person probably meant.
For example, "If I interpret what you said literally, then A. But you probably meant X, so B. If you meant Y, then C."
Depending on how confident you are in your interpretation, you should probably respond to a variety of possibilities. Like if you're < 80% sure that you know what they meant, you should probably respond to possibilities that have at least a 5% chance of being what they meant. I'm not sure whether 80 and 5 are the right numbers, but hopefully it communicates the point.
Why don't people do this?
I see two likely reasons:
Practical considerations