MHB Basic Inequality Prove: $A\leq B\wedge B\leq A \Rightarrow A=B$

  • Thread starter Thread starter solakis1
  • Start date Start date
  • Tags Tags
    Inequality
solakis1
Messages
407
Reaction score
0
Prove:

$A\leq B\wedge B\leq A\Rightarrow A=B$
 
Mathematics news on Phys.org
Trichotomy: Given numbers A and B, one and only one must be true:
1) A> B
2) A< B
3) A= B

Since [math]A\le B[/math], A> B is not true.
Since [math]B\le A[/math], A< B is not true.
 
Is the trichotomy law you are using Equivelant to the following:
$A<B\vee B<A\vee A=B$
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Proof of Inequality: $|a+b| \leq |a| + |b|$
Replies
8
Views
2K
MHB High school inequality 5 abc+acb+bca≥a+b+c.
Replies
5
Views
2K
I Prove Inequality: A,A', B, B' in [0,1]
Replies
2
Views
1K
MHB Proof of Triangle Inequality for $n$ Natural Numbers
Replies
2
Views
1K
I Prove this inequality involving metrics
Replies
1
Views
1K
B What Are Basic Questions About Understanding Inequalities?
Replies
12
Views
2K
I What Are the Benefits of Triangle Inequality in Mathematics?
Replies
2
Views
2K
A Why the triangle inequality is greater than the 2 max{f(x),g(x)}
Replies
1
Views
1K
Prove inequality of a convex function
Replies
3
Views
994
MHB Can Sum to Product Inequalities Hold for Non-Negative Reals?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top