How do we prove the distributive property of multiplication?

Click For Summary
The discussion clarifies that the equation 3 x 2 = 2 x 3 illustrates the commutative law of multiplication, not the distributive law, which is defined as a x (b + c) = a x b + a x c. Proving these laws varies based on the number system used, such as natural numbers, integers, rational numbers, and real numbers, with different complexities involved in each. The most challenging proof involves constructing real numbers from rational numbers, as detailed in Rudin's "Principles of Mathematical Analysis." Some prefer an axiomatic approach to real numbers, where the distributive law is accepted as an axiom rather than proven. Understanding these concepts often requires a foundational knowledge of set theory and the definitions of real numbers.
  • #31
greswd said:
What should I read as prep before Goldrei?
Not sure you will need anything to prep for that, but you may find some of the stuff recommended in this thread useful, in particular the book linked to in post #2 and the 10-page pdf linked to in #5.

I've been discussing similar things with a guy in this thread, and he seems to find both of those useful.
 
Physics news on Phys.org
  • #32
Fredrik said:
Not sure you will need anything to prep for that, but you may find some of the stuff recommended in this thread useful, in particular the book linked to in post #2 and the 10-page pdf linked to in #5.

I've been discussing similar things with a guy in this thread, and he seems to find both of those useful.

That's great, mate. :smile:

Damn, that thread stretched 8 pages.
 
  • #33
I'm struggling with No.5 in Book of Proof.
 
  • #34
greswd said:
I'm struggling with No.5 in Book of Proof.
Chapter 5? Problem 5? You may need to be more specific. :smile:

If it's an exercise that you're stuck on, you can start a thread about it in the homework forum. If it's a concept, you can start a thread in the forum that seems the most appropriate, probably "general math" or "set theory, logic, probability, statistics". Make sure to include the link to the online version of the book and a statement about what specifically you're having difficulties with.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 24 ·
Replies
24
Views
865