Question:
A non-empty sub-set of real numbers which is bounded below has
A non-empty sub-set of real numbers which is bounded below has
Show Hint
Remember: Bounded Below $\rightarrow$ Infimum; Bounded Above $\rightarrow$ Supremum.
Updated On: Jul 3, 2026
- infimum
- Supremum
- both infimum and supremum of A
- neither infimum nor supremum
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept The Greatest Lower Bound (GLB) property states that every non-empty set of real numbers that is bounded below must have a greatest lower bound in $\mathbb{R}$.
Step 2: Meaning This greatest lower bound is formally known as the infimum of the set.
Step 3: Analysis Bounded below means there exists a number $L$ such that for all $x$ in the set, $x \ge L$. The infimum is the largest such $L$.
Step 4: Conclusion Therefore, a set bounded below is guaranteed to have an infimum. Final Answer: (A)
Step 2: Meaning This greatest lower bound is formally known as the infimum of the set.
Step 3: Analysis Bounded below means there exists a number $L$ such that for all $x$ in the set, $x \ge L$. The infimum is the largest such $L$.
Step 4: Conclusion Therefore, a set bounded below is guaranteed to have an infimum. Final Answer: (A)
Was this answer helpful?
0
0
Top AP ECET BSc Mathematics Mathematics Questions
- The integrating factor of $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$ is}
- If $y = y(x)$ is the solution of $\left(\frac{2 + \sin x}{y + 1}\right) \frac{dy}{dx} + \cos x = 0$ with $y(0) = 1$, then $y\left(\frac{\pi}{2}\right) = $
- The solution of $y^{4}dx + 2xy^{3}dy = \frac{ydx - xdy}{x^{3}y^{3}}$ is}
- Which of the following is an integrating factor of $(x^{2} + y^{2} + 2x)dx + 2ydy = 0$?
- The differential equation $\frac{dy}{dx} = \frac{-(x + x^{8} + py^{2})}{y^{8} - y + qxy}$ is exact if}
View More Questions
Top AP ECET BSc Mathematics Real Analysis Questions
- The least upper bound of the set $\{\frac{3n+2}{2n+1}/n\in N\}$ where N is set of natural numbers is}
- Which of the following is a convergent series?
- The function $f(x)=(2)^{\frac{1}{x}}$ is not continuous at}
- If for $x\ne0$ and $f(x)=x^{3}sin\frac{1}{x}, f(0)=0$ then $f(x)$ is}
- \[ \lim_{x\to0}\frac{e^{\frac{1}{x}}}{e^{\frac{1}{x}}+1}=\,\_ \]
View More Questions
Top AP ECET BSc Mathematics Questions
- The integrating factor of $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$ is}
- If $y = y(x)$ is the solution of $\left(\frac{2 + \sin x}{y + 1}\right) \frac{dy}{dx} + \cos x = 0$ with $y(0) = 1$, then $y\left(\frac{\pi}{2}\right) = $
- The solution of $y^{4}dx + 2xy^{3}dy = \frac{ydx - xdy}{x^{3}y^{3}}$ is}
- Which of the following is an integrating factor of $(x^{2} + y^{2} + 2x)dx + 2ydy = 0$?
- The differential equation $\frac{dy}{dx} = \frac{-(x + x^{8} + py^{2})}{y^{8} - y + qxy}$ is exact if}
View More Questions