Since Pi is infinite and non-repeating, would that mean any finite sequence of non-repeating digits from 0-9 should appear somewhere in Pi in base 10?
…and this…
Does any possible string of infinite non-repeating digits contain every possible finite sequence of non repeating digits?
are equivalent statements.
The phrase “since X, would that mean Y” is the same as asking “is X a sufficient condition for Y”. Providing ANY example of X WITHOUT Y is a counter-example which proves X is NOT a sufficient condition.
The 1.010010001… example is literally one that is taught in classes to disprove OPs exact hypothesis. This isn’t a discussion where we’re both offering different perspectives and working towards a truth we don’t both see, thus is a discussion where you’re factually wrong and I’m trying to help you learn why lol.
Is the 1.0010101 just another sequence with similar properties? And this sequence with similar properties just behaves differently than pi.
Others mentioned a zoo and a penguin.
If you say that a zoo will contain a penguin, and then take one that doesn’t, then obviously it will not contain a penguin.
If you take a sequence that only consists of 0 and 1 and it doesn’t contain a 2, then it obviously won’t.
But I find the example confusing to take pi, transform it and then say “yeah, this transformed pi doesn’t have it anymore, so obviously pi doesn’t”
If I take all the 2s out of pi, then it will obviously not contain any 2 anymore, but it will also not be really be pi anymore, but just another sequence of infinite length and non repeating.
So, while it is true that the two properties do not necessarily lead to this behavior. The example of transforming pi to something is more confusing than helping.
it’s not a good example because you’ve only changed the symbolic representation and not the numerical value. the op’s question is identical when you convert to binary. thir is not a counterexample and does not prove anything.
Its not stupid. To disprove a claim that states “All X have Y” then you only need ONE example. So, as pick a really obvious example.
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In terms of formal logic, this…
…and this…
are equivalent statements.
The phrase “since X, would that mean Y” is the same as asking “is X a sufficient condition for Y”. Providing ANY example of X WITHOUT Y is a counter-example which proves X is NOT a sufficient condition.
The 1.010010001… example is literally one that is taught in classes to disprove OPs exact hypothesis. This isn’t a discussion where we’re both offering different perspectives and working towards a truth we don’t both see, thus is a discussion where you’re factually wrong and I’m trying to help you learn why lol.
Is the 1.0010101 just another sequence with similar properties? And this sequence with similar properties just behaves differently than pi.
Others mentioned a zoo and a penguin. If you say that a zoo will contain a penguin, and then take one that doesn’t, then obviously it will not contain a penguin. If you take a sequence that only consists of 0 and 1 and it doesn’t contain a 2, then it obviously won’t.
But I find the example confusing to take pi, transform it and then say “yeah, this transformed pi doesn’t have it anymore, so obviously pi doesn’t” If I take all the 2s out of pi, then it will obviously not contain any 2 anymore, but it will also not be really be pi anymore, but just another sequence of infinite length and non repeating.
So, while it is true that the two properties do not necessarily lead to this behavior. The example of transforming pi to something is more confusing than helping.
We need to start teaching formal logic in grade schools I’m going insane.
Let’s abstract this.
S = an arbitrary string of numbers
X = is infinite
Y = is non-repeating
Z = contains every possible sequence of finite digits
Now your statements become:
it’s not a good example because you’ve only changed the symbolic representation and not the numerical value. the op’s question is identical when you convert to binary. thir is not a counterexample and does not prove anything.
They didn’t convert anything to anything, and the 1.010010001… number isn’t binary
then it’s not relevant to the question as it is not pi.
The question is
Since pi is infinite and non-repeating, would it mean…
Then the answer is mathematically, no. If X is infinite and non-repeating it doesn’t.
If a number is normal, infinite, and non-repeating, then yes.
To answer the real question “Does any finite sequence of non-repeating numbers appear somewhere in Pi?”
The answer depends on if Pi is normal or not, but not necessarily
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