Proof Theory for all real numbers

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SUMMARY

This discussion centers on proving that if \( d = \max\{d_1, d_2\} \) and \( x \geq d \), then \( x \geq d_1 \) and \( x \geq d_2 \) for all real numbers \( d, d_1, d_2, x \). The proof is straightforward, as it follows directly from the definition of the maximum function, which states that \( \max(d_1, d_2) \geq d_1 \) and \( \max(d_1, d_2) \geq d_2 \). Therefore, if \( x \) is greater than or equal to the maximum, it must also be greater than or equal to both \( d_1 \) and \( d_2 \).

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  • Understanding of real numbers and their properties
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  • Basic knowledge of logic and propositional calculus
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  • Learn about logical implications in mathematical proofs
  • Explore propositional calculus and its applications in proofs
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Students in mathematics, computer science, and engineering fields, particularly those studying proof theory and mathematical logic.

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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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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, max(d_1,d_2)\ge d1 and max(d_1,d_2)\ge d2. It follows immediately that if x\ge max(d1,d2) then x\ge d1 and x\ge d2.
 
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!
 

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