Limit help limit of fractional part function power

Click For Summary
SUMMARY

The discussion centers on the limitations of the fractional part function in relation to sums of square roots, specifically examining combinations like sqrt(5) + sqrt(7) and sqrt(3) + sqrt(5). The participants note that while certain combinations yield consistent results, others, such as sqrt(3) + sqrt(11), do not conform to the expected behavior. The need for a general proof that transcends specific cases is emphasized, highlighting the complexity of the topic.

PREREQUISITES
  • Understanding of fractional part functions in mathematics
  • Familiarity with square root properties
  • Basic knowledge of mathematical proofs and conjectures
  • Experience with algebraic manipulation and simplification
NEXT STEPS
  • Research general proofs in number theory related to fractional part functions
  • Explore the properties of irrational numbers and their sums
  • Study advanced algebraic techniques for manipulating square roots
  • Investigate existing literature on the behavior of fractional parts in mathematical functions
USEFUL FOR

Mathematicians, students studying number theory, and anyone interested in the properties of fractional part functions and their applications in algebra.

foxofdesert
Messages
21
Reaction score
0
solved.
 
Last edited:
Physics news on Phys.org
It's also true if you substitute sqrt(5)+sqrt(7) or sqrt(3)+sqrt(5) or sqrt(13)+sqrt(11). I tried sqrt(3)+sqrt(11) and it doesn't seem to be true for that guy, so it's hard to tell but it seems like there should be a general proof that doesn't rely on adding up multiples of sqrt(6) and watching stuff cancel out. I can't fathom what it is though
 

Similar threads

Find limit of multi variable function
  • · Replies 10 ·
Replies
10
Views
2K
Limit on the edge of the domain
  • · Replies 9 ·
Replies
9
Views
2K
A doubt in Partial fraction decomposition
  • · Replies 8 ·
Replies
8
Views
2K
I have troubles finding the limit of this piecewise function
  • · Replies 9 ·
Replies
9
Views
3K
Laplace transform of proper rational function
  • · Replies 6 ·
Replies
6
Views
1K
Taking the Limit of this fraction involving trig functions
  • · Replies 14 ·
Replies
14
Views
2K
Confirm Limit Existence for Function f w/o Piecewise Def.
  • · Replies 4 ·
Replies
4
Views
2K
Use Graph to Determine Limit: Calculating Limits with Piecewise Functions
  • · Replies 3 ·
Replies
3
Views
1K
Calculate the limit cos(x)/sin(x) when x approaches 0
  • · Replies 12 ·
Replies
12
Views
4K
Limit of a fraction as n-> infinity in the numerator and denomominator
  • · Replies 17 ·
Replies
17
Views
2K