# Inspired from Mistakes Give Rise To Problems...

Algebra Level 5

In maths , there exists the following property

$$\left\lfloor \left\lfloor \frac { x }{ 2 } \right\rfloor +\left\lfloor { x }^{ 2 } \right\rfloor \right\rfloor =\left\lfloor \frac { x }{ 2 } \right\rfloor +\left\lfloor { x }^{ 2 } \right\rfloor$$

but if you do

$$\left\{ \left\{ \frac { x }{ 2 } \right\} +\left\{ { x }^{ 2 } \right\} \right\} =\left\{ \frac { x }{ 2 } \right\} +\left\{ { x }^{ 2 } \right\}$$

then this is a big Mistake!!!

but the above expression is true for some set k where k contains all possible values of x from -2 <x<2 and sum of end points of all intervals of k can be expressed as s

Find $$\left\lfloor 100\left\{ s \right\} \right\rfloor$$

Details and assumptions

1.{x} is fractional part of x, which we will define as $$x - \lfloor x \rfloor$$, even for negative numbers.

2.$$\left\lfloor \quad \right\rfloor$$ is greatest integer less than or equal to x.

k$$= \left[ -\frac { 3 }{ 2 } ,-1 \right) \cup \left( \sqrt { 2 } ,2 \right)$$

then s = $$-\frac { 3 }{ 2 } -1+\sqrt { 2 } +2$$

4.Consider both cases whethere end points are open ( ) or closed [ ]

5.This is my second problem ever

6.This problem is inspired from the set Mistakes Give Rise to Problems

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