Math Is Fun Forum

StarShine

Member

Registered: 2012-01-11

Posts: 16

This question doesn't make sense... (Relations...)

Hi guys, I find this confusing. Here's the question: 'is at least as clever as'. The answer is Reflexive and Transitive, but not Symmetric. What I don't understand is how is it Reflexive? You can't be at least as clever as yourself.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: This question doesn't make sense... (Relations...)

hi

i assume you mean the you are using 'is at least as clever as' as a relation.

look at it this way:
if you say 'John is at least as clever as Ann' it means the same as if you said 'John is as clever as Ann or cleverer than her'.

so it's a little like the relation ≥. if you say 5≥3 then it's the same as saying 5>3 or 5=3.

but,you can also say 3≥3,because you need either 3>3 or 3=3.

similarly, if you say 'John is at least as clever as John' we could say this differently as 'John is as clever as John or is cleverer than John'.we know that John can't be cleverer than himself,but he is as clever as himself,and since one condition is satisfied,the statement is true.so John is at least as clever as John (assuming this is the same John)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

StarShine

Member

Registered: 2012-01-11

Posts: 16

Re: This question doesn't make sense... (Relations...)

hi

i assume you mean the you are using 'is at least as clever as' as a relation.

look at it this way:
if you say 'John is at least as clever as Ann' it means the same as if you said 'John is as clever as Ann or cleverer than her'.

so it's a little like the relation ≥. if you say 5≥3 then it's the same as saying 5>3 or 5=3.

but,you can also say 3≥3,because you need either 3>3 or 3=3.

similarly, if you say 'John is at least as clever as John' we could say this differently as 'John is as clever as John or is cleverer than John'.we know that John can't be cleverer than himself,but he is as clever as himself,and since one condition is satisfied,the statement is true.so John is at least as clever as John (assuming this is the same John)

Oh yeaa! I like what you said  " 'John is at least as clever as Ann' it means the same as if you said 'John is as clever as Ann or cleverer than her'. "  That clears things up.

But... here's is what I find awkward. Example, 'is a brother of' That's only Transitive. The funny thing is why is this not symmetric? If Bill is a brother of Steve. Then Steve is a brother of Bill. Or would you have to consider if Bill has a sister?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: This question doesn't make sense... (Relations...)

hi StarShine

but look at this:'Bill is a brother of Julie'

so by symmetry you could be able to say that 'Julie is the brother of Bill'

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.