Undefined for Different Reasons

harpazo65 · 2024-09-09 02:34:03

Nothing a/0 (where a does not equal 0) and 0/0 are undefined, but for different reasons. Explain the different reasons.

Oculus8596 · Yesterday 16:29:15

What have you done so far?

Bob · Today 00:19:02

Division is defined as the inverse process to multiplication.

So, for example, we know that 6 x 8 = 48. This leads to 48 ÷ 8 = 6.

To attach a meaning to 48 divided by 8 we can ask "What number times 8 gives 48?"

So, a/0 would mean asking "What number times 0 gives a?" You cannot find a number to answer this question.

Instead of 0, you could consider a very small number instead of 0. Let's choose a = 6 and divide by 0.1. We get an answer of 60.

Divide by 0.01 and we get 600. Divide by 0.001 and we get 6000. So as the divisor gets smaller the answer gets bigger so we might say as the divisor tends to zero the answer tends to infinity. This is useful when trying to sketch a graph.

What about 0 ÷ 0 ?

For this the question would be "What number times 0 gives 0?" This time there's no shortage of answers as every number times 0 gives 0. So we have to say the answer is indeterminate.

In differential calculus for a general point (x,y) we construct a chord by joining {x,f(x)} to {x + h, f(x+h)} and calculate it's gradient: {f(x+h) - f(x)} / {h}

As h tends to zero this gradient may tend to a limit and that enables us to assume the gradient at the point is that limit. It works for lots of functions, so in those special circumstances 0/0 can be given a value.

Bob

Math Is Fun Forum

#1 2024-09-09 02:34:03

Undefined for Different Reasons

#2 Yesterday 16:29:15

Re: Undefined for Different Reasons

#3 Today 00:19:02

Re: Undefined for Different Reasons

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