Proof Theory for all real numbers

In summary, this is a proof for all real numbers that if d is defined as the maximum of d1 and d2, and x is greater than or equal to d, then x is also greater than or equal to d1 and d2. The proof uses the definition of maximum and basic mathematical reasoning.
  • #1
cannibal
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[SOLVED] Proof Theory for all real numbers

Homework Statement



If a and b are real numbers, we define max {a, b} to be the maximum of a and b or the common value if they are equal.

Prove that for all real numbers d, d1, d2, x, If d = max {d1, d2} and x ≥ d, then x ≥ d1 and x ≥ d2.

Homework Equations





The Attempt at a Solution



I do not know how to even start this problem, i have a small feeling that this exercise has something in relation with the "Logic and propositional calculus topic" but i have not find out were to link it. Any hint or good start will be appreciated.

Thanks :redface:
 
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  • #2
Why in the world is this in "Engineering, Computer Science, and Technology"? Looks like a straightforward math problem to me. First, we have, from the definition, [itex]max(d_1,d_2)\ge d1[/itex] and [itex]max(d_1,d_2)\ge d2[/itex]. It follows immediately that if [itex]x\ge max(d1,d2)[/itex] then [itex]x\ge d1[/itex] and [itex]x\ge d2[/itex].
 
  • #3
Thank you very much "HallsofIvy" i put it here since its a "Computer Science Class" at my college, I am currently studying "Computer Engineer" and i have to take this class.

Thanks!
 

1. What is Proof Theory for all real numbers?

Proof Theory for all real numbers is a branch of mathematical logic that studies the properties of proofs and their formalization for statements involving real numbers. It aims to establish a logical foundation for mathematical analysis and provide a rigorous framework for reasoning about real numbers.

2. How is Proof Theory for all real numbers different from other branches of proof theory?

Proof Theory for all real numbers is unique in that it deals specifically with the properties of proofs for statements involving real numbers. Other branches of proof theory may focus on different types of mathematical objects or logical systems.

3. What are some applications of Proof Theory for all real numbers?

Proof Theory for all real numbers has a wide range of applications in mathematics, computer science, and philosophy. It is used to study the foundations of mathematical analysis, develop automated theorem proving systems, and investigate the philosophical implications of mathematical truths.

4. What are some key concepts in Proof Theory for all real numbers?

Some key concepts in Proof Theory for all real numbers include the notion of a proof, formal systems, axioms, derivations, and logical rules. These concepts are used to construct and analyze proofs for statements involving real numbers.

5. Are there any open problems in Proof Theory for all real numbers?

Yes, there are still many open problems in Proof Theory for all real numbers. Some current research topics include the development of new proof systems for real numbers, the study of proof normalization and proof complexity, and the investigation of the relationship between proof theory and computational complexity.

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