numbers

1. prove that there is no rational number $x$ that satisfies $x^2=2$

I suck at proofs, I don't know why :( I want to improve my mathematics skills, because I like mathematics a lot and want to pursue a career in it. Please check the attached solution and let me know the changes/ way to solve it. Thanks a lot.
2. Probability involving even numbers

If 1\leq p \leq n \; ; n\in \mathbb{N} . find the probability such that p is even number. My approach : P(p-even)=n^{-1}\lfloor \frac{n}{2} \rfloor .
3. Real numbers in (0,1)

Show whether the product of all real numbers in interval (0,1) converges or diverges ?
4. Probability involving square numbers

Let n\leq 111 \: , n\in \mathbb{N} . Find the probability such that n is a square-number and odd . P(n=N^{2} )=?
5. Comparing large numbers without calculus

A curious logical consequence of the principle of non-contradiction is that a contradiction implies any statement; if a contradiction is accepted as true, any proposition (or its negation) can be proved from it. Let's try (*)66^{77} > 77^{66} . I will prove (*) using sgn function(analytic...
6. find the possible numbers

2mn is given.find the value of m and n so that 23mn can by divide by 5 and 8
7. Lucky Numbers

Can someone post an algorithm for Lucky Numbers? Not in any coding language. Just basic English plus Pseudocode(?).
8. Logarithm binary numbers

Hello everyone, I am currently learning about binary numbers and I have stumbled on this problem: "write a function (log n) that calculates the logarithm (base 2) of number n. Number n is a positive binary number". (only using binary arithmetic operations) I know this is a very basic question...
9. Trans-transcendental numbers

According to Wolfram MathWorld: But what if it were the root of a transcendental polynomial itself?
10. Tutoring Arithmetic With Negative Numbers

I'm tutoring a girl who is going into seventh grade, but her is way below that. I haven't seen what she was taught and what her grades were. I asked her what's she's doing in summer. She's said she's in school for Math and ELA (English Language Arts). When I asked if she had any notes or...
11. Book review for Numbers : Numbers: A Very Short Introduction

"Numbers: A Very Short Introduction" by Peter Higgins a book where writer describes different types of numbers. Dear forum member if you have read this book please give me a review . It will be very helpful for me...
12. Law of large numbers

I have a question in statistics. I am a Chemical Engineer (reaction chemistry research). In an example reaction experiment, the feed to a reactor consists of n compounds with mass fractions X1, X2, ... Xn so that: X1+X2+X3+...+Xn=1 This feed goes into the reactor with constant temperature...
13. Square numbers

How many square numbers are in interval [1,999] ?
14. Numbers transformation problem

Hello, I can't figure out the answer to this exercise. It says: 190 -> 42 180 -> 37 160 -> 24 140 -> 16 122 -> 10 154 -> ? Thank you for your help.
15. Probability With the Numbers From 1 to 4 Four Times Each

There are 16 balls, with each number from 1 to 4 four times. Balls are drawn without replacement. How many balls need to be drawn to make at least a 50 percent chance that any one number will have all four balls drawn?
16. Prime ^ Fibonacci ^ partition numbers

What sequence arises from the intersection of prime, Fibonacci and partition numbers?
17. Commonality of Normal Numbers?

Disclaimer...I'm artist not a mathematician;) By the definition of Normal Numbers I'm left with the question, how large of digit strings are shared by all normal numbers? For example the string 14639 should appear in a normal number and in all normal numbers and should likely or inevitably show...
18. Greatest Common Divisor of two specified sequences of numbers (search for equality)

I consider two sequences of numbers $A=\{a_1,...,a_n\}$ and $B=\{k-a_1,...,k-a_n\}$, where $a_1 \le a_2 \le ... \le a_n \le k$. I am looking for such conditions under which: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n)=1$. In more general form: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n) \ge 1$...
19. Prime Numbers and the relationship between n and P_n

We often hear it said that either there is no relation between the natural, or counting numbers, $n$, and their counterparts the primes, $P_{n}$, or that if there is, it is so recondite as to be completely obscure. This is something of a sacred cow, but I don't believe it to be true. I'm not...
20. Programs for floating point numbers to text.

Reference : https://www.google.com/amp/s/www.geeksforgeeks.org/convert-number-to-words/amp/ Can we write computer programs which will convert a floating point or decimal number in words? Programming languages could be C,C++,Java,C#, Python etc. Example : Input 375.50...