Parallel sides?

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JulianMathHelp

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So I was asked if a square had A pair of parallel sides. I know a square has two pairs, but since it says A, I said yes as it does have A pair, but also another pair... Am I correct?

My teacher said it was wrong. She said “a” means “1” in this scenario, and she gave me an analogy: If someone makes 10 hotdogs, did they make A hot dog? She said no... And I agree... but isn’t this anology wrong (it’s a feeling, I don’t really know how to explain it).
 
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In a poker game you have five cards: three queens, a two and five.
If someone asked you if you have a pair and you answered yes, than did you lie?
 
The thing is, my teacher also did a Must be could be geometry thing. The description said one pair of parallel sides, and two sides congruent, though she said that it could be a square. How could it be a square if the description is one pair of parallel sides,
 
JulianMathHelp said:
The thing is, my teacher also did a Must be could be geometry thing. The description said one pair of parallel sides, and two sides congruent, though she said that it could be a square. How could it be a square if the description is one pair of parallel sides,
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A parallelogram contains two pairs of parallel sides. Thus it has a pair of parallel sides.
A trapezoid has a pair of parallel sides but it is not a parallelogram because it does not have two pair of parallel sides.
 
pka said:
A parallelogram contains two pairs of parallel sides. Thus it has a pair of parallel sides.
A trapezoid has a pair of parallel sides but it is not a parallelogram because it does not have two pair of parallel sides.
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Ok, so after pondering about the analogies you made, all of them were yes, including the hot dog one, right?
 
In mathematics, we tend to interpret statements like this inclusively, which is different from everyday life. So, for example, a trapezoid is defined as having a pair of parallel sides, which is (usually) taken to mean at least one pair of parallel sides; therefore, a parallelogram is a trapezoid (it has a pair of parallel sides ... and another, too).

So, yes, we would say that if you made 10 hot dogs, then it is correct to say that you made a hot dog (and another, and another, ...).

What's happening here is that in everyday life we expect people to be as specific as possible, so that if I said I ate a hot dog, you would assume that's all I ate because if I ate more, I would have said so. But I would not be lying in saying "a", just incomplete. The same is true of having two children -- we didn't say only two, so it may be more, though in everyday talk we would commonly assume we are being told about the entire family. It's somewhat ambiguous.

In math we want to avoid ambiguity, so we take a statement as meaning no more than it says: If we say a side, we don't mean only one side. But it's a good idea to say "at least one" when we mean that, for clarity.

Many teachers are not sufficiently familiar with this mathematical way of thinking, and can get it wrong. You are clearly a mathematician at heart.
 
What about for profits? Let’s say someone makes $30 from selling shirts, would it be considered lying or incomplete if they said they made $20? I know this is not math, but it does associate with the same logic.
 
I would say, first, that the context is one that calls for a complete statement, so this would be a lie; and even in a mathematical context, the statement is that the profit is $20, which is a single quantity (true or false), not a part of a set. So if the answer to a problem is 40 minutes, a student would not get credit for giving the answer as 20 minutes!

But, yes, the issue of contextual interpretation can be abused; and even mathematicians have to be real sometimes. If I asked my son to give me the rectangular piece of wood, and he gave me the square, I would probably not thank him even though a square is a rectangle! My intended meaning is clear.
 
Dr.Peterson said:
I would say, first, that the context is one that calls for a complete statement, so this would be a lie; and even in a mathematical context, the statement is that the profit is $20, which is a single quantity (true or false), not a part of a set. So if the answer to a problem is 40 minutes, a student would not get credit for giving the answer as 20 minutes!

But, yes, the issue of contextual interpretation can be abused; and even mathematicians have to be real sometimes. If I asked my son to give me the rectangular piece of wood, and he gave me the square, I would probably not thank him even though a square is a rectangle! My intended meaning is clear.
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I think I understand it now. If someone made $30 from selling shirts, then it would be considered lying if you say you made a profit of $20, as he made a profit of $30. It wouldn't be considered "incomplete" as he didn't make $20 from selling the shirts, he made 30. However, if someone asks the person if the made $20, and they said yes, this is not lying as the person did make $20. I know this sounds contradicting, I don't really know the full reason... It's just a feeling.

Let's make another situation: Someone makes 10 hot dogs. He gives one to his friend. It would be correct to say that he made a hot dog for his friend, right? What if someone asks "how many hot dogs did you make?" The truthful answer would be 10, right? I know it would be considered lying to say like "9" or "8", but I don't really know the reason as the person did technically make "9" hot dogs. If someone asks "did you make 5 hot dogs," and the person said yes, it wouldn't be considered lying, right? But it would be considered misleading?
 
Actually looking back at what I said. I believe money is different from the hot dog analogy as money made is a single definite number while the hot dog analogy is different (like a feeling, not sure how to explain it).
 
This is all part of the subjective aspect of language.

Language doesn't really have absolute rules; we just know what we mean (and someone else might have a slightly different understanding).

In math, on the other hand, we need precise rules, so we modify the language slightly to remove ambiguities. The trouble is, there is a borderland between math and the real world where we need to speak both languages, and things can get confusing. Don't try to make everything in that realm logical -- it isn't!

(Some people, recognizing the ambiguity of language, have tried writing books entirely in symbolic math. It's not a pretty sight.)
 
Just one final thought - it is not considered lying, but misleading if you made 10 hot dogs, and if someone asks you if you made 5 hot dogs, you just say “yes”.
 
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