Fundamental mathematic proofs

  • Thread starter Cheman
  • Start date
  • #1
235
1
Fundamental mathematic proofs....

I know this may seem a slightly odd question, but are there any website or pdf files, etc, floating around of proofs of the basic pricipals and "tricks" of maths? eg - adding, subtraction, multiplication, division, fractional sums and products, percentages, etc? I ask because I feel that these basic bits of maths are often over looked as we are simply told "this is how you do this" - are there any algebraic proofs for these?

Thanks. :wink:
 

Answers and Replies

  • #2
kreil
Insights Author
Gold Member
668
67
I highly doubt there are proofs of these operations. This is because they are the axioms upon which the modern mathematical structure was built upon. Somebody proved (I wish I could remember his name!!) using logic that axioms cannot be proved using themselves, and that given any set of axioms there will be some problems that are true but cannot be proven...by changing the axioms you change which problems can/cannot be proven.
In short, they cannot be proven because they are the basic rules used to prove things. Don't worry-they aren't wrong. They are just the necessary assumptions we have made for centuries.
 
  • #3
453
0
His name was Godel.
 
  • #4
jcsd
Science Advisor
Gold Member
2,090
11
We don't generally prove things like additon, we define them.
 
  • #5
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
132
It depends, however, on what you are actually asking about:

If you are asking:
How can I prove the correctness of the procedure by which we convert a fraction of two naturals into the equivalent decimal representation of that fraction; then this is the same as asking for a proof of Euclid's algorithm which surely exist somewhere.

It is also common in school to call this procedure "division".
 
  • #6
148
0
If I recall correctly there is a proof that 1+1=2. I remember seeing it, it was long and complex. I forget the exact name though, sorry.
 
  • #7
68
0
The proof is in Russell and Whitehead's Principia Mathematica and it is about 168 pages long. It derives 1+1=2 from the axioms of set theory.
 
  • #8
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
These days, 2 is usually defined to be 1+1, so that proof is fairly short. :smile:
 
  • #9
1,056
0
It depends upon what you are asking. They are writers who will tell you about mental math, for example in the formula (X+1)^2 = X^2 +2X +1, this means that if you know 15^2, you can use the formula to find 16^2. Many such "tricks" exist.
 

Related Threads on Fundamental mathematic proofs

  • Last Post
2
Replies
25
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
8K
Replies
1
Views
638
  • Last Post
Replies
3
Views
3K
Replies
1
Views
524
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
1K
Top