0
votes
3answers
139 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 ...
4
votes
3answers
881 views

The set of all infinite binary sequences

Suppose that we have the set $S$ of all possible infinite binary sequences $s_i$ (a sequence is simply an ordered set): $$S=\{s_1,s_2,s_3,\ldots \}$$ where the sequences $s_i$ are like ...
1
vote
2answers
239 views

Harmonic Series Paradox

How to resolve the harmonic series paradox presented in this video by James Tanton?
1
vote
2answers
183 views

sequence of numbers

I remember reading that 'the next number in a sequence of numbers can be anything. It is all about finding the a relation between previous numbers such that the required number becomes next in ...
3
votes
5answers
2k views

Achilles and the tortoise paradox?

Let's say we decide to race on a track 1000km long. You are a 100 times faster than me, meaning if we both start at the beginning you obviously win. To make things more fair you give me a head start ...
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 ...
6
votes
3answers
731 views

Explain why calculating this series could cause paradox?

$$\ln2 = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots = (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots) - 2(\frac{1}{2} + \frac{1}{4} + \cdots)$$ $$= (1 + \frac{1}{2} + ...