# Tagged Questions

154 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 ...
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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 ...
898 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 ...
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How to resolve the harmonic series paradox presented in this video by James Tanton?
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### 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 ...
3k 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 ...
11k views