Magnus Anderson wrote:Not the limit of every number on the right side (that makes no sense) but the limit of the sequence of numbers that is formed by picking one number from the right side of every equation.

You're doing that thing again.

Mathematician: <mathematical fact>

Non-mathematician: <no questions asked, just straight to...> "no, that makes no sense".

Yes it does make sense. The number that's the outcome of each term on the right hand side tends towards a limit of 0 as the denominator tends towards infinity. This is a fact, so just stop with the premature ejaculation and for once try and figure out why it's a fact first before blurting out that it doesn't yet make sense TO YOU and is therefore wrong.

Magnus Anderson wrote:That sequence is \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dotso\) and its limit is indeed \(0\).

If you mean the sequence of each fraction on the right hand side, then yes - that's what I literally just said.

If you mean those are the terms on the right hand side of the equation, then no - that's not what he said.

Either way, shh, listen, learn, and stop pretending.

Magnus Anderson wrote:Silhouette wrote:Add all those limits together to get 0, when the left hand side remains 1 throughout.

Why are we adding those limits together?

Because that's literally the pattern he's trying to communicate and the whole point of his argument maybe?

Magnus Anderson wrote:Let's say that his starting assumption is that an infinite sum of \(\lim_{n\to\infty} \frac{1}{n}\) is equal to \(1\) (even though that doesn't appear to be the starting point of his argument)

It is an incomplete part of the starting point of his argument.

Multiply that limit by "n", and it equals 1.

This is clearly the case for all finite values of "n" on the way to infinity, but not so clear for when "n" is infinite.

Magnus Anderson wrote:then what he is saying is the following:

\(1 = \lim_{n\to\infty} \frac{1}{n} + \lim_{n\to\infty} \frac{1}{n} + \lim_{n\to\infty} \frac{1}{n} + \cdots\)

\(1 = 0 + 0 + 0 + \cdots\)

\(1 = 0\)

The conclusion logically follows from the premises.

The logic is incomplete, as I literally just described.

As I literally just described there are various patterns to use to get to various different conclusions.

Magnus Anderson wrote:But since we know the conclusion is wrong, it follows that some of our premises are wrong. Ecmandu is claiming that the premise that is false is the premise that infinite series converge. I disagree. What's actually wrong is the premise that \(1\) is equal to an infinite sum of limits of the sequence \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dotso\).

The premises are fine, the incomplete logic is wrong. As I literally just described.

He's not even saying that this sequence that you keep repeating is 1.

And infinite series absolutely can converge (either that or they diverge).

Why do you keep talking to me when you keep complaining that I keep calling you out on your bullshit? What did your post just achieve? It's not even clear you understand his simple argument from several things that you're saying and you're still asserting your conclusions as fact without a hint of self-questioning. Some things you're "telling me" when I literally said them just before. And the one question you actually did ask, I literally just answered it in my last post.

Like seriously, what the fuck was that post of yours? A waste of everyone's time, STILL no indication whatsoever that you've adjusted your approach in the slightest to reflect the reality of your expertise on the subject, or that you've learned a single thing, only an attempt to talk to me again to hear what I keep telling you you need to do before this whole thing can even begin to be remotely constructive.