What is the first x value that satisfies x-3>0?

  • Thread starter Thread starter Cinitiator
  • Start date Start date
AI Thread Summary
The discussion revolves around finding the first x value that satisfies the inequality x - 3 > 0. The solution indicates that any value greater than 3, such as 3 plus an infinitesimal number, meets the condition. However, it is noted that there is no smallest real number greater than 3, as real numbers are continuous. The question of whether x is an integer, rational, or real is clarified, confirming that x is a real number. Thus, the concept of infinitesimals is introduced to express values just above 3.
Cinitiator
Messages
66
Reaction score
0

Homework Statement


What's the first x value which satisfies x-3>0?


Homework Equations


x-3>0

The Attempt at a Solution


3 + an infinitesimal number would satisfy this, but I have no idea how to write it down in a proper algebraic form.
 
Physics news on Phys.org
Cinitiator said:

Homework Statement


What's the first x value which satisfies x-3>0?


Homework Equations


x-3>0

The Attempt at a Solution


3 + an infinitesimal number would satisfy this, but I have no idea how to write it down in a proper algebraic form.

What is x? Is it an integer, a rational, a real?
 
Mark44 said:
What is x? Is it an integer, a rational, a real?

x is a real number.
 
There is no smallest real number that is greater than 3.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Solving a nested logarithmic equation
Replies
2
Views
2K
Find integer points on this equation
Replies
8
Views
1K
Query about how the domain of a binomial coefficient was calculated
Replies
2
Views
2K
How to find the range of a function with square roots?
Replies
23
Views
2K
Possible values an expression can take : ##\dfrac{x^2-x-6}{x-3}##
Replies
7
Views
1K
Equation involving 2 variables
Replies
3
Views
2K
Prove relation between the group of integers and a subgroup
Replies
6
Views
1K
[ASK] Trigonometric Inequality
Replies
6
Views
1K
Solve ##\left| x+3 \right|= \left| 2x+1\right|##
Replies
7
Views
3K
Find all possible solutions of x^3 + 2 = 0
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top