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It's the same as: There are more real numbers than you can write down. (Everything you can write down using symbols can only be enumeratable many (you can enume

It's the same as: There are more real numbers than you can write down. (Everything you can write down using symbols can only be enumeratable many (you can enumerate all symbol combinations starting with single symbols), but there are uncountable many real numbers) So now you say: Could you give me an example of such a real number that we can not write down? Answer: No such example can be given because even e or pi or any other real number constructed by an equation is given by just inventing new (countable many) symbols (like π) or by writing down an algorithm which consists of countable many symbols. So to answer your question: There could be problems that can not be explained by math but in the same way you might not even be able express/name/describe the problem.

kumarvvr 8y ago
If framed as a logical equation, wouldnt math explain or have an answer? Sure, i may not write an answer, when thinking from an algebraic perspective, but i sure can answer it from a logical or sets perspective. Perhaps the answer is an empty set?
- laszlokorte 8y ago
  I am not sure I understand what you are saying. If you are speaking of equations you are speaking of symbols right? (∧,∨,¬,...) Whose combinations are only countable many. The answert to what is the empty set?
  - kumarvvr 8y ago
    >Could you give me an example of such a real number that we can not write down? Thst this is a question without any answer can be quantified as a logical equation. The question might not have an answer that is a number, but has a superseding answer thst it is not logically consistent.
  - laszlokorte 8y ago
    Well the answer to: > Could you give me an example of such a real number that we can not write down? Is clearly: No, I can not. But the answer to the question "Are there real numbers that can not be written down in _any_ way" is clearly: yes. If the question is understood as "Is the set of reals bigger than the set of naturals?". So there are cases in which the answer to "can you give me x?" != "is there an x?". So back to you original question: > > not everything can be explained with math > Can you give me any examples? I'm curious. I guess nobody might be able to give you any examples but they could still exist.
laszlokorte 8y ago
The same is true for functions. There exist many more functions (eg ℕ→ℕ) than you can write down because the powerset of ℕ is bigger than ℕ. So it could be that there could be a physical law that the property X of an object is a function of property Y but that function is one which we could not even see as a function because we can not encode it in symbols and probably our brain would not even recognize it as function at all (?)
baddox 8y ago
I’m not sure exactly what you mean by your challenge, but there are several standard examples of noncomputable numbers.
chongli 8y ago
because even e or pi or any other real number constructed by an equation Not true. Most real numbers cannot be constructed at all [1] [2]. There is some interest in replacing the mathematics of real numbers with computable numbers, but this adds additional complexity to analysis (requiring a computable modulus of convergence). [1] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number [2] https://en.wikipedia.org/wiki/Specker_sequence https://en.wikipedia.org/wiki/Specker_sequence
- laszlokorte 8y ago
  Yes that's what I was trying to say with the later part of my setence you quoted: Only coutable many real numbers can be given by name (like pi) or by an algorithm. But there are still many more numbers left which you can not name/point to/give as example.
deleted 8y ago
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kumarvvr 8y ago

If framed as a logical equation, wouldnt math explain or have an answer? Sure, i may not write an answer, when thinking from an algebraic perspective, but i sure can answer it from a logical or sets perspective. Perhaps the answer is an empty set?

laszlokorte 8y ago
I am not sure I understand what you are saying. If you are speaking of equations you are speaking of symbols right? (∧,∨,¬,...) Whose combinations are only countable many. The answert to what is the empty set?
- kumarvvr 8y ago
  >Could you give me an example of such a real number that we can not write down? Thst this is a question without any answer can be quantified as a logical equation. The question might not have an answer that is a number, but has a superseding answer thst it is not logically consistent.
- laszlokorte 8y ago
  Well the answer to: > Could you give me an example of such a real number that we can not write down? Is clearly: No, I can not. But the answer to the question "Are there real numbers that can not be written down in _any_ way" is clearly: yes. If the question is understood as "Is the set of reals bigger than the set of naturals?". So there are cases in which the answer to "can you give me x?" != "is there an x?". So back to you original question: > > not everything can be explained with math > Can you give me any examples? I'm curious. I guess nobody might be able to give you any examples but they could still exist.

laszlokorte 8y ago

The same is true for functions. There exist many more functions (eg ℕ→ℕ) than you can write down because the powerset of ℕ is bigger than ℕ. So it could be that there could be a physical law that the property X of an object is a function of property Y but that function is one which we could not even see as a function because we can not encode it in symbols and probably our brain would not even recognize it as function at all (?)

baddox 8y ago

I’m not sure exactly what you mean by your challenge, but there are several standard examples of noncomputable numbers.

chongli 8y ago

because even e or pi or any other real number constructed by an equation Not true. Most real numbers cannot be constructed at all [1] [2]. There is some interest in replacing the mathematics of real numbers with computable numbers, but this adds additional complexity to analysis (requiring a computable modulus of convergence). [1] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number [2] https://en.wikipedia.org/wiki/Specker_sequence https://en.wikipedia.org/wiki/Specker_sequence

laszlokorte 8y ago
Yes that's what I was trying to say with the later part of my setence you quoted: Only coutable many real numbers can be given by name (like pi) or by an algorithm. But there are still many more numbers left which you can not name/point to/give as example.

deleted 8y ago

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