solvarmedw

2022-10-07

Consider the language $L=\{+,\cdot ,0,1\}$ of rings. It is easy to show using compactness that if $\sigma $ is a sentence that holds in all fields of characteristic $0$, there is some $N\in \mathbb{N}$ such that $\sigma $ holds for all fields of characteristic $p\ge N$. A sort of converse would be, if $\sigma $ is a sentence that holds in all fields of positive characteristic, $\sigma $ is true in all fields of characteristic $0$.

Carson Mueller

Beginner2022-10-08Added 7 answers

The four square theorem yields the following theorem in positive characteristic:

$\mathrm{\exists}a,b,c,d:{a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}+1=0$

$\mathrm{\exists}a,b,c,d:{a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}+1=0$

Tatiana Cook

Beginner2022-10-09Added 3 answers

The canonical solution is to use the fact that ${x}^{2}+{y}^{2}=-1$ has a solution in every finite field, which can be proved by a simple counting argument. That equation is solvable in any field of positive characteristic, because it is solvable in the prime subfield. But not in $\mathbb{R}$.

This is the same idea as the other answer, but the proof of solvability is easier than the $4$-squares theorem.

This is the same idea as the other answer, but the proof of solvability is easier than the $4$-squares theorem.

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???

Use the row of numbers shown below to generate 12 random numbers between 01 and 99

78038 18022 84755 23146 12720 70910 49732 79606

Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?How many different 10 letter words (real or imaginary) can be formed from the following letters

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If x is 60% of y, find $\frac{x}{y-x}$.

A)$\frac{1}{2}$

B)$\frac{3}{2}$

C)$\frac{7}{2}$

D)$\frac{5}{2}$The numbers of significant figures in $9.1\times {10}^{-31}kg$ are:

A)Two

B)Three

C)Ten

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Is power scalar or vector?

What is the five-step process for hypothesis testing?

How to calculate Type 1 error and Type 2 error probabilities?

How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?

1) 9 Hours

2) 3.5 Hours

3) 6 Hours

4) 12.5 HoursWhat is the square root of 106?