Does any transcendental number have infinity different digits of its decimal representation?

shahar

shahar

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Does any transcendental number have infinity different digits of its decimal representation?
Does any transcendental number a fraction?
 
shahar said:
Does any transcendental number have infinity different digits of its decimal representation?
Does any transcendental number a fraction?
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What do you think?

What does "infinity different digits" mean to you? There are only ten possible digits, so infinitely many digits can't possibly be all different; so you must mean something other than what you said.

What kind of number is a fraction? Can that kind of number be transcendental?
 
I mean by the word different digits as you can't guess what the next digit without calculating because there is no pattern you can use. Right?
 
shahar said:
I mean by the word different digits as you can't guess what the next digit without calculating because there is no pattern you can use. Right?
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That is not what "different digits" means.

And the fact that irrational numbers do not repeat does not mean that there is no pattern. A classic example is the irrational number 0.1010010001... . But even a number like pi can be calculated to any number of decimal places; how is "guessing" different from "calculating"? How is "pattern" different from "formula"??
 
Dr.Peterson said:
That is not what "different digits" means.

And the fact that irrational numbers do not repeat does not mean that there is no pattern. A classic example is the irrational number 0.1010010001... . But even a number like pi can be calculated to any number of decimal places; how is "guessing" different from "calculating"? How is "pattern" different from "formula"??
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So, you said that there is no proof that pi hasn't any pattern. Maybe it has but still the mathematicians haven't find it, yet.
 
shahar said:
So, you said that there is no proof that pi hasn't any pattern. Maybe it has but still the mathematicians haven't find it, yet.
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Please explain how do you define pattern? How do you define formula? How do those work (mathematically) "differently" and "similarly"?
 
khansaheb said:
Please explain how do you define pattern? How do you define formula? How do those work (mathematically) "differently" and "similarly"?
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So I find my mistake. Because I can use the word pattern and formula as synonym as:
formula = pattern.
And hence, every thing that hasn't a pattern in one description can be a pattern in other description.
so, Am I understand it clearly?
 
shahar said:
So, you said that there is no proof that pi hasn't any pattern. Maybe it has but still the mathematicians haven't find it, yet.
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Actually I said nothing at all about whether pi has a pattern! Please read carefully!

I asked you how you define your terms, including "pattern"; my understanding is that it has no mathematical definition, so it is meaningless to ask whether pi has a pattern.

shahar said:
So I find my mistake. Because I can use the word pattern and formula as synonym as:
formula = pattern.
And hence, every thing that hasn't a pattern in one description can be a pattern in other description.
so, Am I understand it clearly?
Click to expand...
You certainly aren't expressing your idea clearly. How do you define "pattern"?

And how do you answer my questions in #2??
 
Dr.Peterson said:
Actually I said nothing at all about whether pi has a pattern! Please read carefully!

I asked you how you define your terms, including "pattern"; my understanding is that it has no mathematical definition, so it is meaningless to ask whether pi has a pattern.


You certainly aren't expressing your idea clearly. How do you define "pattern"?

And how do you answer my questions in #2??
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Prof. Ian Stewart uses the word patterns and he said the mathematics that base about Nature based on pattern.
I can't find links to his ideas. Maybe the members of forum will help, so I can define the meaning of patterns in math
 
shahar said:
Prof. Ian Stewart uses the word patterns and he said the mathematics that base about Nature based on pattern.
I can't find links to his ideas. Maybe the members of forum will help, so I can define the meaning of patterns in math
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I assume he uses it as an informal term, not defining it in a way that can be used in theorems. There's a big difference! You will not find the word used in defining irrational numbers, or anything like that.

But why do you refuse to define the terms in your original question, as I asked? You have this habit of migrating from one idea to another without ever settling anything.
 
Dr.Peterson said:
I assume he uses it as an informal term, not defining it in a way that can be used in theorems. There's a big difference! You will not find the word used in defining irrational numbers, or anything like that.

But why do you refuse to define the terms in your original question, as I asked? You have this habit of migrating from one idea to another without ever settling anything.
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I don't know how to define the word pattern.
I can say a pattern is some that repeat on it self like 0.123123123... the pattern is 123 that repeated.
I can give an examples, but no define it.
 
shahar said:
I don't know how to define the word pattern.
I can say a pattern is some that repeat on it self like 0.123123123... the pattern is 123 that repeated.
I can give an examples, but no define it.
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"Pattern", as I have said, is a broad term with no specific definition such that its existence or non-existence could be proved. It includes repetition, along with many other sorts of "pattern" defined by any sort of "rule".

But that word was not used in your original question, which is what I asked about. Have you abandoned that question, and no longer want an answer?
 
I ask if any transcendental number like pi, e (Euler constant) have a pattern or haven't. Is it have reason why it hasn't?
 
shahar said:
I ask if any transcendental number like pi, e (Euler constant) have a pattern or haven't. Is it have reason why it hasn't?
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No, what you asked was
shahar said:
Does any transcendental number have infinity different digits of its decimal representation?
Does any transcendental number a fraction?
Click to expand...
If the first sentence is what you mean by "pattern", the answer is that rational numbers are numbers whose digits repeat (a specific kind of pattern); irrational numbers therefore can't (and that includes transcendental numbers, which are extremely irrational, you might say.

Rational numbers are by definition numbers that can be written as (common) fractions; a transcendental number, being irrational, can't be a fraction.
 
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