The original poster seeks guidance on how to order a set of real numbers from smallest to largest, given that the set has finite members but the specific numbers are unknown. The context appears to involve both mathematical and algorithmic considerations.
Participants are exploring different interpretations of the problem, including the mathematical and algorithmic aspects. Some have provided insights into sorting methods and the nature of sets, while others have raised questions about the clarity of the original question.
There is a mention of constraints regarding the nature of the set, specifically that it must be finite for a smallest or largest member to exist. Additionally, there are references to set notation and the implications of ordering elements within a set.
Cinitiator said:Homework Statement
How to order a set of real numbers, from the smallest to the largest, without knowing any members of the set, but knowing that there are finite members, and that these members are all real numbers?Homework Equations
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The Attempt at a Solution
Tried Googling without any success.
SteveL27 said:Is this for a computer science class? In other words are they after a sorting algorithm?
Otherwise, what does the question mean? You go through the numbers and pick the smallest; then you go through the remaining numbers and pick the smallest; etc.
If you're in an algorithms class they'll be interested in variations of that basic idea. Look up Bubble Sort if you're in a computer science class. But if it's a math class, I don't think I understand the question. Mathematically, the only aspect of this problem that's of interest is that if there are finitely many real numbers, there must be a smallest one. That's not necessarily true for an infinite collection.
(edit)
Is this a notation question? Something like {x_1, ..., x_n in R: i < j => x_i < x_j} ?
I noticed you had another set notation question in a different thread.
Cinitiator said:Thanks for your input.
Let's say that A = {1, 7, 3, 5, 2}
I'm searching for a mathematical operation which would allow me to sort A from the smallest to the largest:
Asorted = {1, 2, 3, 5, 7}
I need this to be able to apply the order statistics operation "max" and "min" on a set, which outputs maximum and minimum extremes of a set, in order to be able to find out the largest number of a set.
To do this, I first need to sort the set, then to apply the max algorithm.
So to find the largest value of the A set, one would write max Asorted, or max{1, 2, 3, 5, 7}.
Unless the set of real numbers is a finite set, there is no smallest member and there is no largest member.Cinitiator said:Homework Statement
How to order a set of real numbers, from the smallest to the largest, without knowing any members of the set, but knowing that there are finite members, and that these members are all real numbers?
Cinitiator said:Thanks for your input.
Let's say that A = {1, 7, 3, 5, 2}
I'm searching for a mathematical operation which would allow me to sort A from the smallest to the largest:
Asorted = {1, 2, 3, 5, 7}
I need this to be able to apply the order statistics operation "max" and "min" on a set, which outputs maximum and minimum extremes of a set, in order to be able to find out the largest number of a set.
To do this, I first need to sort the set, then to apply the max algorithm.
So to find the largest value of the A set, one would write max Asorted, or max{1, 2, 3, 5, 7}.
#include <stdio.h>
int A[] = {1, 7, 3, 5, 2};
int findMax(int []); // prototype for the findMax function
int main(void)
{
int max = findMax(A, sizeof(A));
printf("The largest value is %d", max);
return 0;
}
int findMax(int [] list, int size)
{
// Choose a value that is certain to be smaller than any element in the list.
int max = -1000000;
for (int i = 0; i < size; i++)
{
if (list[i] >= max)
{
max = list[i];
}
}
return max;
}