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.
I see that the context is a different one and i also understand formal logic (contrary to what the other comment on my post says)
It's just that if the topic is pi, I find it potentially confusing (and not necessary) to construct a different example which is based on pi (pi in binary and interpreted as base 10) in order to show something, because one might associate this with the original statement.
While this is faulty logic to do so, why not just use an example which doesn't use pi at all in order to eliminate any potential.
I did realize now that part of my post could be Interpreted in a way, that I did follow this faulty logic -> I didn't