# Boundedness

Boundedness, a concept pervasive across diverse disciplines, encapsulates the essence of limits and constraints within a defined scope. It serves as a fundamental notion in mathematics, where functions are examined for their constraints, as well as in psychology, exploring the boundaries of human cognition and behavior. The term resonates in ecological studies, delineating the confines of ecosystems, and in physics, defining the limitations of physical systems. Boundedness, as a unifying theme, underscores the inherent limitations that shape and characterize various phenomena, contributing a nuanced understanding to fields as varied as mathematics, psychology, ecology, and physics.

Questions

- What are some examples of bounded functions?
- Can an absolute value have a discontinuity #f(x)= |x-9| / (x-9)#?
- Is #y = 5# an upper bound for #f(x) = x^2 + 5#?
- What are some examples of unbounded functions?
- Is there a lower bound for #f(x) = 5 - 1/(x^2)#?
- Suppose #I# is an interval and function #f:I->R# and #x in I# . Is it true that #f(x)=1/x# is not bounded function for #I=(0,1)# ?. How do we prove that ?
- How does the boundedness of a function relate to its graph?
- What is the boundedness theorem?
- Let #f: A rarr B# be an onto function such that #f(x) = sqrt(x-2-2sqrt(x-3)) - sqrt(x-2+2sqrt(x-3))#, then set 'B' is?
- We have #G=(0,oo)#/#{1}# and #x@y=x^(lny)# .How you demonstrate that #forall x,yinG# then #x@yinG#?
- If x is satisfied the inequality #log_(x+3)(x^2-x) < 1#, the x may belongs to the set?
- What parts of set theory are only used in set theory?
- Why does #|x|=-x# as #x -> -oo#?
- If an interval is closed, can it be unbounded?