# Tagged Questions

141 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 ...
121 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: $$x=0.999\ldots$$ $$10x=9.999\ldots$$ ...
110 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 ...
42 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 $d=2$, ...
88 views

### Show that there exist infinitely many primes of the form $6k-1$ [duplicate]

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 $6k-1$