Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

Hmm... question for thought:
Without using modern techniques, other than definitions, how could one make the "method of exhaustion" (used by Euclid and Archimedes) rigorous?
I haven't yet answered this question myself, but I was just thinking about it and thought you peeps might enjoy it.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

Get your **free** account and access **expert** answers to this and **thousands** of other questions

- anonymous

- katieb

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

i think a lot of it comes down to the well ordering principle

- anonymous

actually scratch that, that is for the method of exhaustion used to prove for example that the square root of two is irrational. the method of exhaustion for finding areas is integration

- anonymous

We could try... and you mean like showing that a process terminates using it? But it's more like how does one define an "infinitesimal"? Like how can we make it rigorous?
What does it mean to repeatedly inscribe?
There's an easy definition for a limit (epsilon-delta), but how can we make it useful and rigorous? I think that's the hardest question.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

I mean, the concept is much easier, now that we know calculus, but the case just seems so massively complicated when dealing with it using only elementary operators.

- Kainui

"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. "
-Leonhard Euler

- anonymous

I'm no stranger to calculus. I'm looking for a way to *prove* or show the case of the method of exhaustion to be mathematically rigorous using axiomatic, rather than intuitive, principles and definitions.

Looking for something else?

Not the answer you are looking for? Search for more explanations.