Indeterminate: the hidden power of 0 divided by 0

Great video, I rate it 0/0. Full marks!

this man sort of comes across as a bond villain but is friendly enough so that I think he would be the assistant to the bond villain and would end up somehow disarming the nukes of the villain as a sort of double agent. these are the things I thought about in college. and I wonder why my degree didn't work out.

The person who invented 0 gave nothing to mathematics

Now I can sneak up on zero

4:09 "but as long as it's staying off 0..." Nice! You'd be surprised how rare people explain this important piece of information when they explain derivatives

The real reason that you are advised to avoid indeterminate forms is that your must invoke L'Hôpital's Law -- which you will not be able to pronounce to to everybody's satisfaction.

"Noone would know Isaac Newton. That would be really sad, right?" I bet Leibniz wouldn't agree.

My takeaway from this is that, because "0/0" is undefined or indeterminant, it can be anything -- and thus we have to look at it in context to see what value it makes sense to be (if sense can indeed be made). I've never thought of this that way, but it makes sense! And it makes sense not just in calculus, but linear algebra, too, where the determinant of a matrix being 0 means it has multiple possible values for an inverse as well. Heck, this even puts kernels of homeomorphisms in abstract algebra into context, as well, where you can describe the spaces of things that go to 0!

I asked Siri what 0 divided by 0 is, and it broke my heart. Siri why are you so cold!!

Newton should be getting more credit because the term he used for derivatives/velocities was cooler: fluxions.

You're a fantastic teacher. In less than a minute I went from not being sure why dividing by zero doesn't actually work to completely getting it.

Best T Shirt Ever.

As an aeronautical engineering student I find it extremely satisfying to see stuff I am learning at the university.

Poor Leibniz never gets any credit

Just want to say that your explanation that both 1 and infinity are both functions just cleared up a lot of confusion about infinity for me and opened my mind to a totally new way of thinking about numbers. Thanks!

5:49 THAT'S FUN

In his book “Yearning for the impossible” one my favourite authors John Stillwell says “…mathematics is a story of close encounters with the impossible and all its great discoveries are close encounters with the impossible.” I hope you like the examples of such close encounters in this video. I actually put up a version of this video earlier today. About three minutes later twenty of you pointed out a REALLY silly typo. Just could not live with that, hung my head in shame, pulled the video and fixed it. Here it is again. Hope you like it. One more thing, if you contribute a translation into a language other than English, could you please let me know by sending an e-mail to [email protected]. YouTube is not very good at notifying me when new subtitles are waiting for me to approve. Also, please add your names at the beginning of the subtitles. A lot of people are asking about the t-shirt and the missing bits at the bottom. If you are interested have a look: shirt.woot.com/offers/how-natural-selection-works?…

Another good one Mathologer. The closing moments were the most important IMO: aspiring mathematicians and those interested should always remember that they're free to redefine expressions and loosen axioms depending on their area of work - much new material can be discovered in this way (e.g. NE Geometry). Similar arguments made for defining what 0**0 should be, and different answers depending on who you ask of course. Perhaps even video worthy :) Thanks again, have a good one.

I love this representation of 0/0... It gives me a great deal of context that touches on many other ideas I find familiar. You are doing a fantastic job, and I look forward to every new video( as well I find I play the most intriguing many times over.) Thank you for your passion, inspiration, and creativity.