Results 1 to 9 of 9

Math Help - More on Binary Operations

  1. #1
    Banned
    Joined
    Sep 2009
    Posts
    502

    More on Binary Operations

    We know that addition, subtraction, multiplication, and divisision are binary operations.

    Question:
    Is raising a number to a power also a binary operation?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    It is, because you must have a base and a power. You can think of binary operations as a predicate, or a function: a + b = sum(a,b). Similarly, exponentiation would have to look like this: x^y = power(x,y). A binary operation is like a function with two arguments. Make sense?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Sep 2009
    Posts
    502
    Quote Originally Posted by Ackbeet View Post
    It is, because you must have a base and a power. You can think of binary operations as a predicate, or a function: a + b = sum(a,b). Similarly, exponentiation would have to look like this: x^y = power(x,y). A binary operation is like a function with two arguments. Make sense?
    Yes sir, it does make sense since binary operation is a function \mathbb{R} \times\mathbb{R} \rightarrow \mathbb{R}.

    Now, since min(\delta, 1)= \delta \vee 1, it seems to me that it follows the function \mathbb{R} \times\mathbb{R} \rightarrow \mathbb{R}.

    Does it mean that min(\delta, 1)=\delta too is a binary operation?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Here you have to be careful. Are you talking about the function \min(x,y)? Or the function f(\delta)=\min(\delta,1)? The first is binary, the second unary.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Sep 2009
    Posts
    502
    Oh, yes, I was indeed very careless.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Sep 2009
    Posts
    502
    Quote Originally Posted by Ackbeet View Post
    Here you have to be careful. Are you talking about the function \min(x,y)? Or the function f(\delta)=\min(\delta,1)? The first is binary, the second unary.
    Now, instead of \min(x,y), I reverse it to x*y= \max(x,y) in  \mathbb{Z}. For this, I think 0 is an identity of (\mathbb{Z},*)since \max(x,0)=x and \max(0,y)=y.

    Again, if I change it to x*y= \max(x,y) in \mathbb{N}. Will it be correct to say the 1 is an identity of (\mathbb{N},*) since there is no integer less that 1?

    My thinking is that if [tex]x>1, then \max(x,1)=x and if x=1, nothing has changed \max(x,1)=x.

    Yah?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    If by \mathbb{Z} you mean all the integers, then 0 is not the identity, because \max(-1,0)=0, not -1. The identity would have to be -\infty, which is not in \mathbb{Z} unless you consider the "extended integers". I've never seen that, though I have seen the extended reals.

    Now, if you consider \mathbb{N}, then you definitely do have an identity with the max function, as you say. You should be careful, incidentally, in your words. You meant, "There is no natural number less than 1." I would agree with your identity in this case.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Banned
    Joined
    Sep 2009
    Posts
    502
    Thanks again sir. You have taught me that mathematics is all about little details. Hmm, -\infty \not \in \mathbb{Z}--that's interesting. I was tempted to ask why, but I know it belongs to another thread, and perhaps it's just beyond my scope of understanding at this point.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    ...mathematics is all about little details...
    Details can sure be important! However, you have to be able to see the big picture as well. They're both important.

    I once had a math professor who was a mathematical physicist. He was one of the most engaging lecturers I've ever had. He said that the way to get good at mathematics is to work in a high-energy physics lab. You have these 10,000 volt wires running around. If you make a mistake, you're dead. He said that's the way you should approach math.

    Take it for what it's worth.

    You're welcome for whatever help I was able to provide. Have a good one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Binary Operations
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 10th 2010, 04:17 PM
  2. Binary operations, groupoids
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 10th 2010, 05:16 AM
  3. Binary Operations, check please :)
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 8th 2010, 09:31 AM
  4. Binary operations?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 15th 2008, 02:26 PM
  5. Binary Operations!
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 7th 2008, 10:22 AM

Search Tags


/mathhelpforum @mathhelpforum