What is the meaning of c = min {a, b/M} in IVP proofs?

In summary, the notation c = min{a, b/M} represents the minimum value between a and b/M, with a being associated with the x-axis and b/M being associated with the y-axis on a graph. This notation is commonly used in real analysis to find the minimum value in a set. However, it is important to note that if the set does not have a minimum value, then "min S" is undefined.
  • #1
hawkingfan
24
0
Hey dudes, I'm trying to understand the proofs about IVPs in the appendix of my differential equations book but I can't understand this notation that says c = min {a, b/M}.

What is that notation supposed to mean? I'm guessing that it stands for minimum value between a and b/m. (a is associated with the x-axis and b/M is associated with the y-axis based on the picture of the graph in the book) I'm just beginning to study real analysis so I haven't seen this notation yet.
 
Physics news on Phys.org
  • #2
Yes it just means to take the minimum value between a and b/M.

In general x = min{y1,y2,y3,...,yn} means to take the minimum value from the set {y1,y2,y3,...,yn}.
 
  • #3
"min S" is the element of S that is less than every other element -- it's minimum.

(the domain of "min" consists only of those ordered sets with a minimum. In other words, if S doesn't have a minimum, then "min S" is undefined)
 

1. What does the notation "x" mean?

The notation "x" typically represents a variable, which is a symbol used to represent a quantity that can change or take on different values in a mathematical or scientific expression. It is often used in equations to indicate the unknown value that needs to be solved for.

2. What does the notation "f(x)" mean?

The notation "f(x)" is used in mathematics to represent a function, which is a relationship between two variables. The "f" typically stands for "function" and the "x" represents the input value. So, "f(x)" means "the value of the function at x".

3. What does the notation "∑" mean?

The notation "∑" (sigma) is the symbol for summation, which is a mathematical operation that involves adding up a series of numbers. It is often used in statistics and calculus to represent the sum of a set of values.

4. What does the notation "∫" mean?

The notation "∫" (integral) is used in calculus to represent integration, which is the process of finding the area under a curve. It is also used to represent the anti-derivative, which is the original function that would give the derivative of a given function.

5. What does the notation "μ" mean?

The notation "μ" (mu) is often used in statistics to represent the mean, which is the average of a set of numbers. It can also be used to represent other important values, such as the population mean or the coefficient of friction in physics.

Similar threads

I Understanding a proof of inexistence of max nor min
    • Calculus
Replies
4
Views
883
MHB -b.2.2.26 IVP min value y'=2(1+x)(1+y^2); y(0)=0
    • Differential Equations
Replies
3
Views
1K
Confusing max(min(f(x,y)) notation?
    • Calculus
Replies
4
Views
2K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
    • Calculus and Beyond Homework Help
Replies
3
Views
521
I Attempting to find an intuitive proof of the substitution formula
    • Calculus
Replies
7
Views
1K
Calculus Differential Equations book recommendations
    • Science and Math Textbooks
Replies
5
Views
2K
What is the meaning of g: [a, b] → R in set notation?
    • General Math
Replies
2
Views
894
What does a delta symbol mean in mathematics?
    • Calculus
Replies
2
Views
5K
I Why does the author use the notation ##f_c(d)## instead of ##f(c,d)##?
    • General Math
Replies
4
Views
1K
A What is the meaning of "excess" Goldstone bosons?
    • Quantum Physics
Replies
3
Views
795

Hot Threads

Recent Insights

Back
Top