0
votes
1answer
47 views

Are distance-related paradoxes limited by the size of an atom?

See these 2 paradoxes: Coastline paradox The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. ...
2
votes
1answer
34 views

Could you explain Perron's paradox to me, please?

This is Perron's paradox: Let $N$ be the largest integer. If $N > 1$, then $N^2 > N$, contradicting the definition of $N$. Hence $N = 1$. What does it mean? I get from it that a very large ...
0
votes
3answers
137 views

Infinity and Hilbert's hotel paradox

I did some infinite series calculations while studying Fourier analysis and the concept of infinity really bugs me. I haven't read or heard not one sensible explanation yet (for me), what infinity ...
2
votes
0answers
73 views

Paradox of Infinity? [duplicate]

If a series such as '$a$' below adds to infinity: $a = 1 + 2 + 4 + 8 + 16 + \cdots\to \infty$ Multiplying '$a$' by $2$ yields: $2a = 2 + 4 + 8 + 16 + \cdots\to \infty$ However when I subtract ...
1
vote
3answers
243 views

Random Point on Infinite Line Paradox

I've invented a paradox, or at least I think I have. Here is how it goes: On an infinite line, a point is placed at random. You start at point 0 on the line, and your job is to find the point, but ...
1
vote
2answers
234 views

Harmonic Series Paradox

How to resolve the harmonic series paradox presented in this video by James Tanton?
13
votes
4answers
3k views

Two paradoxes: $\pi = 2$ and $\sqrt 2 = 2$ [duplicate]

Possible Duplicate: Is value of $\pi = 4$? Can anyone explain how to properly resolve two paradoxes in this YouTube video by James Tanton?
14
votes
1answer
520 views

Is there an absolute notion of the infinite?

Skolem's paradox has been explained by the proposition that the notion of countability is not absolute in first-order logic. Intuitively, that makes sense to me, as a smaller model of ZFC might not be ...
44
votes
7answers
11k views

Infinity = -1 paradox

I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1: Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 ...
31
votes
5answers
4k views

How can a structure have infinite length and infinite surface area, but have finite volume?

Consider the curve $\frac{1}{x}$ where $x \geq 1$. Rotate this curve around the x-axis. One Dimension - Clearly this structure is infinitely long. Two Dimensions - Surface Area = ...