Does the Empty Set Contain Zero and the Zero Vector?

  • Thread starter Thread starter pivoxa15
  • Start date Start date
  • Tags Tags
    Empty Set
pivoxa15
Messages
2,250
Reaction score
1

Homework Statement


Does the empty set contain 0, the zero vector, ... all zero elements of a non empty set?


Homework Equations





The Attempt at a Solution



I don't think so. But could be wrong. The empty set shoudn't contain anything whatsoever.
 
Physics news on Phys.org
The empty set is empty, it contains nothing, so it does not contain 0, it does not contain any zero vectors, etc.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Showing that the empty set is subset of every set
Replies
6
Views
1K
Setting a family of sets equal to the empty/null set?
Replies
6
Views
3K
A proof the Empty Set is unique
Replies
8
Views
7K
Can the empty set be used to satisfy inf(B) ≥ sup(B)?
Replies
2
Views
4K
Prove that x is in S or x is an accumulation point of S
Replies
25
Views
3K
Why is the Cartesian Product S×T Empty When T is Empty?
Replies
6
Views
2K
Is the Set {x^2 - x, 3 - x^2, 1 + x} a Vector Subspace of P^2(x)?
Replies
29
Views
2K
Elementary Set Theory (Discrete)
Replies
1
Views
1K
Relations, power sets and the empty/null set.
Replies
1
Views
2K
Proof with sets and elements. Am I going about this right?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top