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sologuitar

Member

Registered: 2022-09-19

Posts: 467

Undefined For Different Reasons

College Algebra
Section R.1

Both (a/0), where a does not equal 0 and 0/0 are undefined, but for different reasons. In your own words explain the different reasons.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Undefined For Different Reasons

Division is defined as the inverse operation to multiplication, so any division can always be re-written as a multiplication.

a/b = c may be re-written as a times c = b.

If we try to determine a numeric value for 0/0 re-write it as a multiplication:

If 0/0 = x then we want to find x so that 0 times x = 0. There is no single solution to this so x cannot be determined.

If a/0 = b then a times b = 0.  The only solution for this is a = b = 0.
For all other values of 'a' no 'b' exists at all (different from the above as here we have no solutions whereas above we have multiple solutions.)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Undefined For Different Reasons

A great, simple reply. Thank you, Bob. Can you please type the steps needed for me to upload math photos here? Why not program the site to have a more up-to-date method for uploading photos, which is so important for students? The geometric interpretation helps out a great deal.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Undefined For Different Reasons

Sorry about the image problem.  The old server did allow images to be upoaded but that was lost when MathsIsFun switched us to a new server.  I use Imgur and uload images there; then link using bcc.  There's a post about this here http://www.mathisfunforum.com/viewtopic.php?id=28084

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Undefined For Different Reasons

Bob,

Thank you for the link. I don't have a computer or laptop.
Can I upload pictures using my android phone? I will try to upload one or two photos following the steps provided in the link.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Undefined For Different Reasons

Bob,

I see that you are the only member answering my questions. Is there anyone else who can help you? It just doesn't seem right for one person to do all the math work. I do show effort when the question is not over my head.