What they lack is ability (or at the very least, incentive) to abandon logic when dealing with this subject.
The subject isn’t so complicated that it requires mathematical expertize. You don’t need mathematical expertize to understand that “2 + 2 = 4”. A bunch of mathematicians can’t declare that “2 + 2 = 5” and claim that the dissenters are wrong because they are merely amateurs.
The claim is that the two symbols ((0.\dot9) and (1)) do not represent the same quantity. A number of arguments have been put forward. You’re supposed to point out their flaws. The quoted doesn’t do that.
It’s important to note that it’s not necessary to show why Wikipedia proofs are wrong. There’s a much simpler proof that shows that they must be wrong – whatever their real flaws are.
I’m examining Wikipedia proofs for fun, not out of necessity. I might, in fact, be wrong about why Wikipedia proofs are flawed, but such a scenario wouldn’t render the main proof (which is a very simple proof) invalid.
This isn’t to say that I’m not sure about my claims regarding Wikipedia proofs. I’m pretty confident about them.
Thankfully, not everything is complicated in life, so not everything requires extensive proofs.
Again, the above isn’t pointing out flaws within an argument.
That’s correct.
((9 + \underline{0.\dot9}) \div 10 \neq \underline{0.\dot9})
The two underlined numbers don’t have the same number of 9’s.
In other words, the two infinite sums don’t have the same infinite number of non-zero terms.
Therefore, they aren’t the same number.
That’s my claim. It’s up to other people (which includes you) to point out flaws within my argument if they wish to do so.
That’s precisely the point of our disagreement. The (0.9) in (s) is paired with (0.09) in (s \div 10).
Let’s take (9.\dot9) and divide it by (10) and see what we get:
$$
9.0 \div 10 = 0.9\
0.9 \div 10 = 0.09\
0.09 \div 10 = 0.009\
\cdots
$$
I don’t wonder, I know. You suffer from low tolerance threshold. Not something to be proud of.
Considering that you talk about it publicly, yes.
If you can’t accept that Hilbert’s Hotel is nonsense, there is, I am afraid, no hope for you.
Notice that it’s not merely counter-intuitively full and not full. It does not merely go against intuition. It goes against logic.
Intuition is neither right nor wrong on its own. It’s that thing that is sometimes wrong and sometimes right. You can never know. So if a claim is counter-intuitive, it does not necessarily mean that it’s right or that it’s wrong. But if it goes against logic, then we have a problem, Sir.
A hotel that is both full and not full. Not a logical contradiction at all.
Now you’re conflating different concepts. Infinity/endless is not the same as indeterminate/undefinable.
That’s not true.
If you can’t determine whether there is a difference between two numbers, it does not follow that there is no difference between them.
Sorry to disappoint you.
Here’s a couple of super simple arguments for you to address. And when I mean “address”, I mean “point out their flaws”.
The argument that “Infinite quantity A - 1 < Infinite quantity A”.
viewtopic.php?p=2754790#p2754790
The argument that Hilbert’s Hotel is nonsense:
viewtopic.php?p=2754844#p2754844
Let me see you (or anyone else) point out their flaws.