Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
There is one final topic that we need to address as far as solution sets go before leaving this section. Consider the following equation and inequality.
x2 + 1 = 0
x2 = 0
If we limit ourselves to just real solutions (that we won't always do) then there is no solution to the equation. Squaring x makes x greater than equal to zero, after that adding 1 onto i.e that the left side is guaranteed to be at least 1. In other terms, there is no real solution to this equation. For the similar basic reason there is no solution to the inequality. Squaring any real x makes it positive or zero and thus will never be negative.
We required a way to mention the fact that there are no solutions here. In solution set notation we say that the solution set is empty & denote it with the symbol : ∅ . This symbol is frequently called the empty set.
In the discussion of empty sets we supposed that were only looking for real solutions. Whereas i.e. what we will be doing for inequalities, we won't be limiting ourselves to real solutions with equations. Once we get around to solving out quadratic equations (x2 + 1 = 0) we will let solutions to be complex numbers & in the case looked at above there are complex solutions to x2 + 1 = 0 . If you don't know how to search these at this point i.e. fine we will be covering that material in some sections. At this point simply accept that x2 + 1 = 0 does have complex solutions.
Lastly, as noted above we won't be utilizing the solution set notation much in this course. This is a nice notation & does have some use on occasion especially for complicated solutions. Though, for the vast majority of the equations & inequalities which we will be looking at will have simple sufficient solution sets that it's just easier to write the solutions and let it go at that. Thus, that is what we will not be using the notation for our solution sets. Though, you have to be aware of the notation & know what it means.
NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and
20+20
Describe about Parallel and Perpendicular Lines ? Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect. The bl
explain the basics of permutation
find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month
All things considered, in a sense of ethnicity (a sense of identification with and loyalty to one's group) good or bad? is it harmful or helpful? What would be lost if Americans lo
What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems
Q4. Assume that the distance that a car runs on one liter of petrol varies inversely as the square of the speed at which it is driven. It gives a run of 25km per liter at a speed o
The null hypothesis It is the hypothesis being tested, the belief of a specific characteristic for illustration, US Bureau of Standards may walk to a sugar making company along
The Rank Correlation Coefficient (R) Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among tw
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd