Tagged Questions
2
votes
0answers
61 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
2answers
132 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
104 views
Harmonic Series Paradox
How to resolve the harmonic series paradox presented in this video by James Tanton?
1
vote
2answers
130 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 ...
1
vote
3answers
347 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 ...
38
votes
7answers
4k 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
620 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} + ...
