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

solakis1 · Dec 9, 2020

Prove:

$A\leq B\wedge B\leq A\Rightarrow A=B$

HOI · Dec 9, 2020

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.

solakis1 · Dec 9, 2020

Is the trichotomy law you are using Equivelant to the following:
$A<B\vee B<A\vee A=B$

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

Discussion

Graduate Expected numbers of cards of a last color remaining

Graduate Probability puzzle

Undergrad The problem of points

Undergrad The countability paradox of computable numbers

Undergrad How does axiom of foundation prevent infinite sequence of elements?

Graduate Cannot understand this corollary on surreal numbers

High School Bunkbed Conjecture Debunked?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

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

Discussion

Similar threads

Proof of Inequality: $|a+b| \leq |a| + |b|$

High School Some trouble understanding this basic inequality proof

How is the inequality |a+b| \leq |a| + |b| proven using different methods?

How Does the Epsilon Argument Prove \( a \leq b \)?

Prove Inequality with Mean Value Theorem: |\sin a - \sin b| \leq |a - b|