I like your quote and I see where you're coming from, especially given that I'm talking so informally. While I do not have the ability to formally pre...
Mathies keep the fun stuff to themselves. :P Thanks for checking it out! I'm glad you like the approach. I have not looked into SIA. However, just a f...
It's only obvious to me because I only know a handful of real numbers so I assume you're talking about sqrt(2). But it's not a matter of laziness, no ...
I liken it to physics. Many engineers get by with classical physics. They don't worry that it predicts singularities because it works great for them i...
Because I'm lazy, I'm going find the velocity of the particle instead of acceleration. First, I want to show you three valid graphs of y=t3-5t2+9t-6 (...
I find this example unsatisfying given that everything important is contained in the ellipses. You are no better just writing "For instance: ... just ...
@"norm": Thanks for the book recommendations, I plan to read both "Analysis By Its History" and "Groundless Grounds". Very poetic, I like it! To me it...
@"GrandMinnow": Imagine having a discussion with a child. If they ask a question, one way of addressing it is to add layers of complexity to the issue...
When I say potential infinite, I don't mean 'something that might be infinite'. I mean a process that certainly goes on to no end. We are certain that...
Can you give me an example of what would break down without non-computable numbers? I like that you admit that there are ugly weeds. So you're just sa...
Perhaps we are both making this 'scenic trail' unpleasant for the other in different ways. Do you want to live in a country where the 'scenic trails' ...
Imagine that lines are fundamental, not composite objects. Take a string and mentally label the two endpoints -? and ?. In my world, this string only ...
How can we travel from one point to the another without traversing through the intermediate points in sequence? This is essentially Zeno's paradox and...
You can't tell by inspecting the digits, but at least 0.999... is computable so you can make some assessments by comparing the algorithms used to gene...
I think he's touching on something important. If time can be broken down into a collection of instants and if at one instant we're stationary and the ...
The eternal truths that I am referring to are different from your eternal truths because mine are finite. I don't need to assert the existence of an a...
You are equating 'approaching' with 'arriving at'. If I could only tell you one piece of information about my trip I would tell you my destination. Bu...
My ideas are so many steps away from a formal mathematical theory and in any one of those steps my ideas can be revealed to be inconsistent or useless...
Thanks jgill! Stack Exchange is a good format for Q&A but I don't think it offers a very good format for discussion. I think TPF is a pretty sweet spo...
Our disagreement is also due to us having different definitions of approach. We both agree that y gets lower and lower (and perhaps you would even agr...
I believe that the only measurable states of a proposition are true or false so in one sense I accept the Law of the Excluded Middle. Where my view de...
This is where the misunderstanding is. Nobody is saying that there is a final destination or that (?,0) exists. The standard definition of a limit doe...
He only proved that ?2 is not a rational number. He did not prove that ?2 is an irrational number. Yes, I'm concerned with proof by contradiction. If ...
Hmm, you've revealed that my original post was quite vague. I believe that an object exists if it is being computed. I exist as an artifact of the law...
Perhaps I don't grasp it, or perhaps I just don't agree with it. Let's assume it's the former. Please tell me whether the following points aligns with...
Your notion of 'close' that is based on the number of points between A and B can only have value in a number system which is not dense in the reals, s...
It seems like you're implying that finite math is equally paradoxical by comparing the infinitely long needle with an infinitely long horn. If you wan...
Most of the area is on the "needle" portion but most of the volume is enclosed by the "horn" portion. I find it odd that you're focusing on the needle...
Consider the Stern-Brocot tree. If L=1/2, LL=1/3, LLL=1/4, and so on, then L_repeated is a "real number" which it cannot be less than. I suspect you'l...
You are essentially saying that it takes <3.15 ft3 to paint the finite horn AND it takes >3.15 ft3 to paint the finite horn. If film thickness doesn't...
I don't see the paradox - as long as we're allowed to play with the thickness we can come up any combination of numbers for the finite horns. What's i...
Let me clarify this...there's something better than giving a numerical measure....the best we can do is to stick with an algorithm which defines a pot...
The surface area of the horn has no limit - as we consider larger and larger horns that area continues to increase, so we can loosely say that it has ...
As everyone on this thread knows, the reason why calculus was reformulated based on limits was to avoid talking about infinitesimals (and actual infin...
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