0
votes
2answers
114 views

Is Continuum Hypothesis false? [closed]

The continuum hypothesis states that there is no set whose cardinality is strictly between that of the integers and the real numbers. However, it seems that it is possible to construct sets that ...
0
votes
1answer
111 views

$0.999999\ldots=1$? Others? [duplicate]

I have seen this problem come up many times and I was wondering if my proof is valid for $0.999\ldots=1$ where $0.999\ldots$ is continuous: $$x=0.999\ldots$$ $$10x=9.999\ldots$$ ...
0
votes
2answers
95 views

Does sum of all natural numbers contradict another rule?

I must say that I am not a mathematician, just a enthusiast who likes to read all the "weird" results in mathematics. I read that sum of all natural number equals to $-1/12$ and I am also aware that ...
0
votes
1answer
38 views

map sum of square integers to a contiguous range of integers

Given a list $a$ of integers, $$n_{a_1}, n_{a_2}, ..., n_{a_d}$$ have $$N_a = \sum_{j=1}^d n_{a_j}^2.$$ The various $N_a$, $N_b$ etc. are integers, but are not contiguous: for example, if $d=2$, ...
2
votes
1answer
80 views

Show that there exist infinitely many primes of the form $6k-1$

This is a question on the text book that i have no way to deal with. Can anyone help me? Show that there exist infinitely many primes of the form $6k-1$
1
vote
1answer
119 views

Why prime number theorem tends to one

I am curious about prime numbers so i just started reading about it. While reading some articles i came across prime number therom (PMT) which states like this $\displaystyle \lim_{n \to \infty} \pi ...
4
votes
2answers
104 views

Infinite shots fired in a lattice forest

A hunter is standing in the center of an infinite 2D forest. There are point trees at all the integer lattice points. The hunter fires a gun with a bullet of zero width in a random direction. He ...
2
votes
0answers
71 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 ...
3
votes
1answer
139 views

How to prove that $0.01001100011100001111…$ is not periodic decimal number?

I have the following decimal number: $0.01001100011100001111...$ Notice how whenever we have one 0, we also have one 1, two 0's, two 1's, etc. How do you continue it to infinity and prove that this ...
2
votes
2answers
227 views

What is the use of such concepts as potential infinity and actual infinity?

I'm aware of such mathematical concepts as and potential infinity and actual infinity. But I do not understand how those concepts are being used. Are there any applications to such concepts? Are there ...
-1
votes
2answers
241 views

Is there such math concept as potential zero?

It seems that I need to use concept of potential zero in my work and I want to know whether I could reference some other works in order to fully understand what I'm dealing with. Specifically for my ...
5
votes
5answers
765 views

Repeating digits in $\pi$

As $\pi$ has infinite digits in its decimal expansion, one could argue that its digits will repeat after a finite number of digits. If so, it is a rational number. What's wrong with this argument?
15
votes
2answers
583 views

Is there an infinite number of primes constructed as in Euclid's proof?

In Euclid's proof that there are infinitely many primes, the number $p_1 p_2 ... p_n + 1$ is constructed and proved to be either a prime, or a product of primes greater than $p_n$. Trivially, we ...
6
votes
2answers
548 views

Infinite Prime Proof Using Euler's Totient

I need something explained or corrected: In my number theory class we proved that there are an infinite number of primes using Euler's Phi Totient. It went something like this: Let $M = p_1 p_2 ...
21
votes
4answers
950 views

You are standing at the origin of an “infinite forest” holding an “infinite bb-gun”

I use stories like these to develop intuition... or perhaps to destroy it. I have my own answers in mind, but I want to see if I have made any mistakes... You are standing at the origin of an ...