2007-06-28 13:31:06 · 7 answers · asked by jumba 1 in Science & Mathematics ➔ Mathematics
Such insightful answers from the first two respondents! rofl.
A relation is a set of points (a,b), where each of a and b are from some set S. The kind of ordered pairs (a,b) are entirely unrestricted.
For example, we could define a relation on real numbers by "x is related to y" if x
A function is a similar set of points (a,b), where we write b=f(a). The set of points is restricted, however. There can only be ONE ordered pair for every a. In other words, if (a,b) and (a,c) are in the relation, (a,b)=(a,c) or simply b=c.
So clearly, not all relations are functions. For example, the unit circle is not a function on the Cartesian plane.
Now, if there is only one set S from which the a's and b's are drawn, any function is a relation. Like real-valued functions of real numbers - these are always relations because the x and y values are all real numbers.
However, we often have functions from one set onto an entirely unrelated set. In that case, it isn't exactly a relation. A relation MUST be defined on ONE set only. For example, I could define a function from the set of my pets onto the real numbers, where I number them from 1 to 5 based on weight. I can't call that a relation, because the ordered pairs don't have components from the same set.
One way though to rectify this though: if it were a function from set A to set B, it would be a relation on the set AUB.
So functions are, basically, relations, although you have to be careful about the sets in which the relations/functions are defined.
What's the reason? Well, I've given you the reason (you know, instead of a terse unhelpful answer). I hope I've helped.
2007-06-28 13:42:55 · answer #1 · answered by сhееsеr1 7 · 1⤊ 0⤋
Yeah I've seen all those arguments before; nice cut-and-paste job, you probably got all those from a homosexual-friendly website. Those are actually twisting the message around to claim the opposite of what they really say. Many places God says marriage is between a man and a woman. In fact Jesus even reiterated it: Matthew 19:4-5 – 4"Haven't you read," He replied, "that at the beginning the Creator 'made them male and female,' 5and said, 'For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh'? Show me anywhere in the bible where God says two of the same sex should be united together.
2016-05-22 01:49:52 · answer #2 · answered by ? 3 · 0⤊ 0⤋
Function is always a relation.
f(x)=
Relation is not a function because you could have y^2 = x^2 and solve it for y, then get y=+/- x.... that is, y=x or y=-x. You get TWO functions instead of one. Then, both combined can not be a function of one equation.
2007-06-28 13:45:19 · answer #3 · answered by tkquestion 7 · 1⤊ 1⤋
Yes to first no to second. The definition of a function is a relation such that every element in the domain is related to exactly one element in the range.
2007-06-28 13:39:09 · answer #4 · answered by Sean H 5 · 1⤊ 1⤋
Yes, a function is always a relation because a relation, as its name say, merely relates two unknowns.
No, a relation doesn't necessarily have to be a function.
Functions must either be one-to-one (ie one x value for one y value) or many-to-one (ie many x values for one y value).
2007-06-28 13:40:19 · answer #5 · answered by Kemmy 6 · 1⤊ 1⤋
Functions: for each answer y = F(X) (Range) there is only one X (Domain) that fits.
Relations: for each answer y = F(X) (Range) there can be many X's (Domain) that fit.
2007-06-28 13:40:36 · answer #6 · answered by telsaar 4 · 1⤊ 1⤋
Yes. No. Definition.
2007-06-28 13:34:44 · answer #7 · answered by Mark 6 · 0⤊ 2⤋