consider this problem:
"Given a TM $X$, determine if the language accepted by $X$ contains more than $100$ strings"
Is this problem decidable or not?
Opinion 1: (mine)
I derived my proof by using Rice's Theorem. Let P be the property "The language has more than 100 words" this is a non trivial propriety as long as I can find a language that has less than 100 words, so we can conclude that the given problem is not decidable.
Opinion 2: (friend of mine)
We know that the language is accepted by the TM so by definition it's a semi-decidable language, but we know that a language is semi-decidable iff it is enumerable so we can use the enumeration algorithm and check if it produces at least 100 strings, so it is decidable.
Which one is right?
Your friend's idea only shows that this problem is recursively enumerable : you can check that the language has at least 100 words when it does, but you'll be left trying indefinitely if it does not.