I am Student , from INDIA. Today, I have to give seminar on a problem "There exist a Language over Sigma that is not a Recursively Enumerable" and from the past one week I was searching the solution in an easy way to explain this to students of my class and to my respective teacher. And you solved my problem. That contradictions you have given are best to explain these concepts. Thank You SO mucH SIR!
how does a language that consists of finite length words, is infinite in size itself : epsilon, a, b , ab, ba , aa, bb, aaa, aab ... , this means that at some point, the words come to an end because the length of the words is finite, how does the set become infinite in size then (need explanation)
Yeah it's weird. A language over an alphabet with N symbols and strings no larger than M has at most M^N strings. If the strings are of finite length it would mean that the language has at most (some finite number)^(some finite number) strings, which is also a decidedly finite quantity.
Can a language have an infinite amount of strings? If not, why would you need an infinite binary string to specify it? And if every language can be specified by a finite binary string, and there are countably many finite binary strings, isn't the amount of languages countably infinite? The finite binary strings will be of different lengths, but you could just pad them with 0s to make them all the same length as the longest finite binary string. Wait, but for every finite binary string I guess you could ask the question "given this slightly longer string, is it in the language?" and then your specifier string would have to grow to encapsulate the answer to that question (even though I imagine the answer will always be 0). So you need an infinite binary string, at least in theory, to specify a language. I'm not sure this is right, so I'm posting my comment anyway even though I guess I agree with the conclusion.
You taught me something in 15 minutes what my professor took 2 lectures! Mind Blown!!!
Finally found someone with clear and concise explanation, who doesn't stretch the video to 30 min. Thank you!
Wow. The contradictions are real, but they eventually solved the mastery! Thanks for the great video tutorial.
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I am Student , from INDIA. Today, I have to give seminar on a problem "There exist a Language over Sigma that is not a Recursively Enumerable" and from the past one week I was searching the solution in an easy way to explain this to students of my class and to my respective teacher. And you solved my problem. That contradictions you have given are best to explain these concepts. Thank You SO mucH SIR!
You are awesome, Sir
Wow. I’m going to watch some more. It seems like you’re working your way to Godel’s incompleteness. Excellent!
Such a nice man.
Doesn't that mean that the set of non-Turing -recognizeable languages is uncountably infinite?
this is an awesome video!!
just beautiful
how does a language that consists of finite length words, is infinite in size itself : epsilon, a, b , ab, ba , aa, bb, aaa, aab ... , this means that at some point, the words come to an end because the length of the words is finite, how does the set become infinite in size then (need explanation)
Yeah it's weird. A language over an alphabet with N symbols and strings no larger than M has at most M^N strings. If the strings are of finite length it would mean that the language has at most (some finite number)^(some finite number) strings, which is also a decidedly finite quantity.
Imagine a language consisting of words {e, a, aa, aaa, ...}, over an alphabet {a, b}. This language is infinite in size but each element is finite.
Can a language have an infinite amount of strings? If not, why would you need an infinite binary string to specify it? And if every language can be specified by a finite binary string, and there are countably many finite binary strings, isn't the amount of languages countably infinite? The finite binary strings will be of different lengths, but you could just pad them with 0s to make them all the same length as the longest finite binary string.
Wait, but for every finite binary string I guess you could ask the question "given this slightly longer string, is it in the language?" and then your specifier string would have to grow to encapsulate the answer to that question (even though I imagine the answer will always be 0). So you need an infinite binary string, at least in theory, to specify a language.
I'm not sure this is right, so I'm posting my comment anyway even though I guess I agree with the conclusion.
Thanks sir
great!
comp sci is too hard is even worth doing
bozo