At this point the same errors are recurring indefinitely, like this new (10^{-\infty}) notation still treating infinity like a finite quantity.
As Ecmandu correctly pointed out, there is no last (10^{-1}) in what that’s supposed to denote, just the same as there is no last (1) in (0.\dot0{1})
Until something comes up that hasn’t already been disproven (\lim_{n\to\infty}10^n) times over, I’m gonna go ahead and leave the nonsense peddlers to it.
If you don’t like the notation (merely because you don’t understand it, I must say), you may consider its equivalent which is (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots). That’s a “valid” numerical representation, isn’t it?
I’ve already stated it but you conveniently ignored it opting instead to focus on what you don’t understand.
It seems like you’re one of those rare people who can understand Ecmandu
There is no last (1) in (0.\dot01). The product (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots) is infinite. The end is merely in the symbol.
My post about 1/10 ever being expressed implied your argument of 1/101/101/10… etc…
I thought I could have used short hand, but it doesn’t bother me that we’re trying to be precise here, so, I apologize for the shorthand.
So here’s the deal: “carrying” is when you carry numbers from right to left. This is first grade math.
If I have a number like 99+2… the 2 plus the last 9 is 11. The one gets deposited in the solution column and the 10 gets carried over to the left in the tens column as a 1. 1+9 equals 10, which you put in front of the one that you already have the the solution column, to equal 101.
Sure. But how is that relevant? That was my question.
Why do you mention carrying?
It’s obvious that you’re talking about the standard algorithm of adding numbers together. The question is: why?
Are you trying to use the standard algorithm to add (0.999\dotso) and (0.000\dotso1) together? If so, why?
Do you think that you can prove that there is no difference between (0.999\dotso) and (1) by proving that the standard algorithm of adding numbers together can’t be used to add (0.999\dotso) and (0.000\dotso1) together?
Actually I’ve known all this math since over half my life ago, and I have been regularly keeping up with advanced level maths to this day for fun - I actually really enjoy it.
The problem here though is if others aren’t close enough to the same level, they aren’t going to recognise this and will just assume it’s just another bogus claim from some randomer on the internet because they don’t know any better.
I’m dealing with a self-professed non-mathematician here and it shows. All he has left anymore is “you just don’t understand”, and when I say/prove that I do, he can just respond with incredulity and keep repeating the accusation. That’s all this thread is now - non-mathematicians claiming long-time competent mathematicians don’t understand, whilst repeating the same schoolboy mistakes over and over. Other competent mathematicians here recognise these mistakes too, and keep advising the non-mathematicians that they’re wrong and I’m right. But our old-friend “the backfire effect” is just making them double down harder because admitting you’re wrong is hard for people since it requires emotional maturity and intellectual honesty to overcome the cognitive dissonance. That’s why there’s no longer any point in me trying to help them anymore - they don’t want it.
I only recently learned all the MathJax code to express the math nicely on this forum though - I already thanked Magnus for his only contribution so far of bumping the post from a couple of years ago that mentioned it and linked to its documentation. I also unequivocally accept the utility of exploring what happens when you take something that doesn’t work mathematically, and treat it as something that does work - as I’ve mentioned several times by now. All I’m doing is explaining exactly why it doesn’t work mathematically - I’m not even against doing it anyway because that’s where new math can be born, but there’s still a couple of people left who find even that too much to accept.
See, I’m humble enough to give credit where credit is due, and I’m simply honest about people being wrong when they are.
There’s plenty of topics on this forum that I leave alone because I don’t know enough about them - you won’t find me reading up last minute on those topics and claiming expertise there, and you’ll only find me claiming expertise when I actually have it, such as here. There’s far better mathematicians out there than me, but the dissenters here most definitely aren’t one of them.
Yes, that’s where we agree. Where we disagree is whether or not infinities come in different sizes. You think that they don’t (that’s where you agree with SIlhouette.)