Guy, you need to chill the fuck out.
Like I said, just because “you don’t see the connection yet, don’t presume there is none, let me explain it to you” - do you agree that “presumption is the seed of all sin” like you said, or not? You’re so convinced of some combination of malevolence, incompetence, psychological or political compromise on my part that you refuse to see other quite obvious explanations as to how hard it seems to be to have a simple discussion. Stop presuming so I can unpack this for you, and it will all come together for you unless you don’t want to see it do so, which won’t be my fault.
We calm now? Great. We can continue
To briefly address this one before we get to the actual content, I thought it was fairly straight forward, but as before I have simply been misinterpretted and presumed to be distracting. People ask if they can query something if they think they see the source of some disagreement in said something, no? I proceded to that source, to query whether it shined any light on what’s going on here. Like I said, there’s a connection between all the things I’m saying that I’m trying to bring together in a way that gets to the bottom of our disagreement. If you’d let me explain it to you, you’d see it too. I apologise for not being as literal and concise as you seem to need me to be, ok? I’m trying.
Right, great. Query answered! Easy, right?
Let’s ride this momentum, shall we? It doesn’t mean the rest of my post is nonsense, it just means it doesn’t necessarily get to the bottom of things as directly as I suspected and wanted to test.
I felt I had, you disagree. This is fine, don’t flip the fuck out.
To be clear, I’ve been well aware of the formula (x + y)^2 = (x^2 + 2xy + y^2) since I learned and repeatedly applied it correctly while at school.
You took my method of expanding (x+y)^2 as something like just “2xy”, or just “x^2 + xy” - only part of the full process at any rate & missing “subtotals” as you say, which makes sense from the way you’ve perfectly correctly presented it.
May I please request, at this point, for you to agree or disagree whether this adequately encapsulates where you think I went wrong? May I also please request if you think I’ve sufficiently acknowledged and shown understanding of the point of your contention?
If so, I invite you to consider the scenario where x = y, as done all the way back on page 4:
Using the same form as I did above just now, we now get (x + x) * (x + x) = (x^2 + 2xx + x^2)
Do you agree that this can also be written as (x^2 + 2xx + x^2) = (x^2 + x^2 + x^2 + x^2)?
More specifically, on page 4 we were covering the case that x = y = 1
so since (x + x) * (x + x) = (x^2 + x^2 + x^2 + x^2)
we have (1 + 1) * (1 + 1) = (1^2 + 1^2 + 1^2 + 1^2)
this can be written as (1 + 1)^2 = (1 + 1 + 1 + 1)
Am I right? Do you agree there has been no funny business or “switching up” so far?
A similar thing occurs when you have (1+1+1)^2 = (1^2 + 11 + 11 + 1^2 + 11 + 11 + 1^2 + 11 + 11)
Obviously the right hand side can be expanded to (1+1+1+1+1+1+1+1+1)
As I said in this post: "Consider the example (1+1+1+…+1), is it agreed that the “…” represents an endless string of “1+1"s?”
We covered the examples of (1+1)^2 = (1+1+1+1) and (1+1+1)^2 = (1+1+1+1+1+1+1+1+1). I’m sure you don’t need any more examples of adding an extra 1 each time to solve (1+1+1+1)^2 and so on?
So we ought to be able to jump all the way to (1+1+1+…+1)^2, I feel.
Each time we progress towards this from (1+1)^2, through (1+1+1)^2, through (1+1+1+1)^2 and so on, we get an answer that can be written as (1 + “some finite number of zeroes” + 1)^2 = (1 + “some other finite number of zeros” + 1)
I want to stress that in these finite examples, I acknowledge that “some finite number of zeroes” on the left hand side is not the same as “some other finite number of zeroes” on the right hand side.
Are we in agreement that I acknowledge this and there is still no funny business or “switching up” so far?
The problem is once you transcend these finite examples to the infinite, by the definition of infinity you can no longer bound “some finite number of zeroes” or “some other finite number of zeroes” - they are both endless. There is not an end to either, such that one’s end can be longer or further than another.
Are we in agreement that this is where you think the funny business happens?
My argument is that if you stick strictly to the definition of infinity, (1+ "infinite zeroes +1)^2 = (1+ "infinite zeroes + 1)
That is to say, (1+1+1+…+1) * (1+1+1+…+1) = (1+1+1+…+1)
As I understand it, you distinguish infinite, endless strings of 1s being added up from other infinite, endless strings of 1s being added up. Are you in agreement with this?
You represent the rationale by showing the relation that finite examples show as you tend towards infinity, which is correct.
You represent the rationale by showing the construction of the infinite examples and how they are constructed differently, which is also correct.
Do you agree that I acknowledge your rationale fairly and accurately?
Do you agree that I understand where our arguments diverge?
Do you agree that infinity, by definition has no bounds in order to say one is larger or goes further than another?
Do you agree that this on topic and relates to where you think I made a mistake here: