Proving Equation: m + (n + (p + q)) = ((m+n) + p) + q

  • Thread starter Thread starter mossfan563
  • Start date Start date
Click For Summary
SUMMARY

The equation m + (n + (p + q)) = ((m + n) + p) + q is proven using the associative property of addition. The discussion emphasizes the importance of applying the associative property, which states that (a + b) + c = a + (b + c), rather than the commutative property. The user initially attempted to manipulate the equation using commutativity but was advised to focus on associativity for a successful proof. This clarification is crucial for understanding the correct approach to proving the equation.

PREREQUISITES
  • Understanding of the associative property of addition
  • Familiarity with the commutative property of addition
  • Basic knowledge of mathematical axioms and properties
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the associative property of addition in depth
  • Practice proofs involving the commutative and associative properties
  • Explore examples of using axioms in algebraic proofs
  • Learn about the distributive property and its applications
USEFUL FOR

Students studying algebra, mathematics educators, and anyone interested in understanding the properties of addition and their applications in proofs.

mossfan563
Messages
54
Reaction score
0

Homework Statement


I have to prove this equation:
m + (n + (p + q)) = (m + n) + (p + q) = ((m + n) + p) + q

Homework Equations


Commutative property of addition and multiplication
(m+n) = (n+m), (mn) = (nm)
Associative property of addition and multplication
(m+n)+p = m+(n+p), (mn)p = m(np)
Distributive property
m * (n+p) = mn + mp

The Attempt at a Solution


Only being allowed to use certain axioms, I ruled out all except the ones in the relevant equations.
So far I'm pretty much stumped as to how to prove the equation. Going from the first part to the second is difficult. I tried to manipulate the first part of the equation to use commutative and I got nowhere. How do I get myself in the right direction?
 
Physics news on Phys.org
You should use associativity, not commutativity.
 

Similar threads

Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
  • · Replies 3 ·
Replies
3
Views
2K
Prove ##a \cdot 1 = a = 1 \cdot a## for ##a \in \mathbb{N}##
  • · Replies 1 ·
Replies
1
Views
2K
Prove ##1 + a=s(a)=a+1## for ##a \in \mathbb{N}##
  • · Replies 1 ·
Replies
1
Views
2K
Proving Completeness property of ##\mathbb{R}## using Dedekind cuts
  • · Replies 20 ·
Replies
20
Views
4K
Proofs By Induction: Proving P(n) for All n
  • · Replies 3 ·
Replies
3
Views
2K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
  • · Replies 3 ·
Replies
3
Views
2K
Prove ##a + b = b + a## using Peano postulates
  • · Replies 3 ·
Replies
3
Views
2K
Order of a^m when gcd(m,n) = 1
  • · Replies 2 ·
Replies
2
Views
2K
If p is even and q is odd, then ##\binom{p}{q}## is even
  • · Replies 19 ·
Replies
19
Views
4K
For any n, m given ##I_n \thicksim I_m##, prove that ## n=m##
  • · Replies 2 ·
Replies
2
Views
1K