Inequality Proof: Max {A+B,C} ≤ Max {A,C} + Max {B,C}

  • Thread starter Thread starter stanley.st
  • Start date Start date
  • Tags Tags
    Inequality
AI Thread Summary
The inequality Max {A+B,C} ≤ Max {A,C} + Max {B,C} is under scrutiny for its validity with real numbers A, B, and C. It is confirmed to hold true when A, B, and C are nonnegative. However, counterexamples arise when negative values are introduced, indicating that the inequality does not universally apply. The discussion suggests exploring specific cases where Max {A+B,C} equals A+B or C to identify scenarios that challenge the inequality. Overall, the inequality's validity is conditional and requires careful consideration of the values involved.
stanley.st
Messages
30
Reaction score
0
Hello,

i've met during problem solving with inequality

\max\{A+B,C\}\le\max\{A,C\}+\max\{B,C\}

where A,B and C are real numbers. I don't know whether it holds, but I need to prove that.

Thanks for reply...
 
Mathematics news on Phys.org
It holds if A,B,C are nonnegative, but play around with some negative numbers and you'll find a counterexample. (Hint: Does the inequality always hold if max{A+B,C}=A+B, or if max{A+B,C}=C? Pick the case you can't prove easily and search for counterexamples there.)
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

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 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

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
MHB Prove the inequality (a^3-c^3)/3≥abc((a-b)/c+(b-c)/a)
Replies
3
Views
2K
MHB Find a,b,c,d for Max $a+b-c+d$
Replies
1
Views
1K
MHB Inequality - find the largest K in (a+b+c+d)^2≥Kbc
Replies
7
Views
2K
MHB Prove Inequality: $\sqrt{ab}+\sqrt{cd}\le \sqrt{(a+d)(b+c)}$
Replies
1
Views
1K
MHB How to Prove the Inequality for a, b, and c in the Range of 0 to 1?
Replies
5
Views
2K
MHB Find the minimum a^4+b^4+c^4−3abc
Replies
2
Views
1K
MHB Inequality of logarithm function
Replies
3
Views
1K
MHB Inequality of logarithm function
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top