Mixing
Degrees of freedom in a space containing finite points
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Consider a 2-dimensional grid with m horizontal lines and n vertical lines where m and n are finite positive integers. They intersect m*n points. Consider a set of the intersection points. What is the number of degrees of freedom of this set?
My thinking is that if I were to name each point in the set using integers from 1 to m*n, then I can uniquely identify any point with just this one variable. Therefore, my degree of freedom is one. However, I've been told that finite sets have 0 degrees of freedom and an infinite continuous set is required to define a degree of freedom. So, what exactly is the exact definition of degrees of freedom?
linear-algebra
asked Jan 23 at 8:12
MouliMouli
61
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add a comment |
$begingroup$
Consider a 2-dimensional grid with m horizontal lines and n vertical lines where m and n are finite positive integers. They intersect m*n points. Consider a set of the intersection points. What is the number of degrees of freedom of this set?
My thinking is that if I were to name each point in the set using integers from 1 to m*n, then I can uniquely identify any point with just this one variable. Therefore, my degree of freedom is one. However, I've been told that finite sets have 0 degrees of freedom and an infinite continuous set is required to define a degree of freedom. So, what exactly is the exact definition of degrees of freedom?
linear-algebra
asked Jan 23 at 8:12
MouliMouli
61
$endgroup$
add a comment |
$begingroup$
Consider a 2-dimensional grid with m horizontal lines and n vertical lines where m and n are finite positive integers. They intersect m*n points. Consider a set of the intersection points. What is the number of degrees of freedom of this set?
My thinking is that if I were to name each point in the set using integers from 1 to m*n, then I can uniquely identify any point with just this one variable. Therefore, my degree of freedom is one. However, I've been told that finite sets have 0 degrees of freedom and an infinite continuous set is required to define a degree of freedom. So, what exactly is the exact definition of degrees of freedom?
linear-algebra
asked Jan 23 at 8:12
MouliMouli
61
$endgroup$
Consider a 2-dimensional grid with m horizontal lines and n vertical lines where m and n are finite positive integers. They intersect m*n points. Consider a set of the intersection points. What is the number of degrees of freedom of this set?
My thinking is that if I were to name each point in the set using integers from 1 to m*n, then I can uniquely identify any point with just this one variable. Therefore, my degree of freedom is one. However, I've been told that finite sets have 0 degrees of freedom and an infinite continuous set is required to define a degree of freedom. So, what exactly is the exact definition of degrees of freedom?
linear-algebra
linear-algebra
asked Jan 23 at 8:12
MouliMouli
61
asked Jan 23 at 8:12
MouliMouli
61
asked Jan 23 at 8:12
MouliMouli
61
asked Jan 23 at 8:12
MouliMouli
61
asked Jan 23 at 8:12
MouliMouli
61
61
add a comment |
add a comment |
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