Instructors who take great offense

[pka]

No, a set does not have to be defined in numerical order. A set may not even consist of numbers so how can you order it numerically. Nor can a set of complex numbers be ordered. https://en.m.wikipedia.org/wiki/Set_(mathematics)
However, I have seen people define sets to be ordered. Moreover, it is useful to show orderable sets in their "natural" order. Unless the instructions specified to write down the set in ascending numerical order, your daughter was correct, and the teacher was wrong. It will not be the first time that she will have to put up with someone in authority making a mistake.

I fear that teacher has no idea that sets are not ordered. If so the teacher will take great offence at told s/he in incorrect.

 

[JeffM]

I fear that teacher has no idea that sets are not ordered. If so the teacher will take great offence at told s/he in incorrect.

You are, sad to be said, almost certainly correct.

Long ago, I went to my son's first grade teacher-parent meeting. I was sat in a chair that placed my head at about knee-height to the teacher, an obvious attempt to establish a dominance relation. While sitting at this woman's feet, I was told that my son asked too many questions. I retreated into close to an hour of absolute silence. My wife was not amused.

About the same time, I attended a parent-teacher conference for my daughter, who was in kindergarten. My daughter apparently talked too much, but the teacher thought that she might eventually learn to be silent, or at least less obtrusive, if my wife and I only strove diligently to curb my daughter's young tongue. (Unfortunately, my wife and I did not take the teacher's advice, but that failure is now the burden of my daughter's husband.) When we were leaving the kindergarten building, the evening star floated in the autumn sky. The teacher said, "Oh, how beautiful that star is, yet an infinite light years away." This was, I suppose, an attempt to demonstrate the "sensitivity" of the teacher. In a fit of lack of deference, I responded that it was a planet, not a star, and that the observable universe was bounded. My wife was amused this time, but not much.

After those two incidents, my wife refused to tell me when there were parent-teacher conferences, let alone suggest that I attend. She has always been a wise wench.

 

[pka]

You are, sad to be said, almost certainly correct.
Long ago, I went to my son's first grade teacher-parent meeting. I was sat in a chair that placed my head at about knee-height to the teacher, an obvious attempt to establish a dominance relation. While sitting at this woman's feet, I was told that my son asked too many questions. I retreated into close to an hour of absolute silence. My wife was not amused.

I got two talks of of this.
I think it was a second grade paper.
The top is the blank question. Instructions: Color half the pie.
The bottom is what our daughter turned in.
It was marked incorrect. So I wrote a note simply saying "sinse when 4/8 is not 1/2?
In talks to In-service teachers I asked "What is a solution?"

 

[JeffM]

I got two talks of of this.
I think it was a second grade paper.
View attachment 10256 The top is the blank question. Instructions: Color half the pie.
The bottom is what our daughter turned in.
It was marked incorrect. So I wrote a note simply saying "sense when 4/8 is not 1/2?
In talks to In-service teachers I asked "What is a solution?"

Oh my.