I'm posting this blog early because I am going to be out of town over the weekend.
What was difficult for me?
A function f from a set A to a set B is called one-to-one or injective. if every two distinct element of A have distinct images in B.
One to one was tough to understand at first, but then I made sense of it! I understand it that there are unique values for the response, that you can't plug in a 1 and get a 2, and then plug in a 4 and get a 2. That would make the function not one-to-one.
A function A -> B is called onto or surjective if every element of the codomain B is the image of some element of A. This was difficult for me to understand. I will need more help on understanding this.
Bijective or a one-to-one correspondence functions are both one-to-one and onto. This seems alright to understand, once I understand onto. The book says, again, "if every element of the codomain B is the image of some element of A."
This website seems to help me out a lot..... http://www.regentsprep.org/Regents/math/algtrig/ATP5/OntoFunctions.htm
What did I find interesting?
I took linear algebra at one point, and I learned all of these things for the first time. I didn't really understand it at that time. Now I'm beginning to understand it. Onto and one-to-one are really interesting ways to think about functions. Learning about all of these different ways to classify functions are helping me understand more about functions. That's what I find really interesting - finding different ways to understand functions. I thought I knew a lot about functions, but I didn't really. Learning about these different types of functions hopefully really help me.
What was difficult for me?
A function f from a set A to a set B is called one-to-one or injective. if every two distinct element of A have distinct images in B.
One to one was tough to understand at first, but then I made sense of it! I understand it that there are unique values for the response, that you can't plug in a 1 and get a 2, and then plug in a 4 and get a 2. That would make the function not one-to-one.
A function A -> B is called onto or surjective if every element of the codomain B is the image of some element of A. This was difficult for me to understand. I will need more help on understanding this.
Bijective or a one-to-one correspondence functions are both one-to-one and onto. This seems alright to understand, once I understand onto. The book says, again, "if every element of the codomain B is the image of some element of A."
This website seems to help me out a lot..... http://www.regentsprep.org/Regents/math/algtrig/ATP5/OntoFunctions.htm
What did I find interesting?
I took linear algebra at one point, and I learned all of these things for the first time. I didn't really understand it at that time. Now I'm beginning to understand it. Onto and one-to-one are really interesting ways to think about functions. Learning about all of these different ways to classify functions are helping me understand more about functions. That's what I find really interesting - finding different ways to understand functions. I thought I knew a lot about functions, but I didn't really. Learning about these different types of functions hopefully really help me.
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