The Language of Mathematics (4): The Real Number Set - Part 2

[NickSolo420]

how on earth do you hold up the chalk to exactly the point that you want to illustrate on the board behind you?

[chychochycho]

Magic...also known as looking at the small screen on the camera :)

[pinedavideos]

I love your videos. I hope you become more popular. I'll be watching many more and sharing with whoever is interested. Also, quick question, what is 2.22 repeating as a fraction? 2 + 22/100 doesnt seem right :P

[chychochycho]

if you mean 2.22, then it equal 2 +22/100, but you have to reduce 22/100. So it's actually 2+11/50

if you mean 2.2222222222...., then it's 2+2/9

[KelferMookie]

This guy is good...I am finally understanding this stuff, and actually think I may like it.

[eduardosayas]

Your a genious you should have books,TVshows,vids,and maybe prob some private lessons to other kids. You Rock. Your strategy is like no other. : ) u help me man.

[chychochycho]

Thanks, glad to be of service :)

As for your recommendations, I'll work on them :)

[dizzytrizzy07]

2:20 - 2:45 : it's just funny cuz he looks like "irritated" to the people who owe sheep x) heehee. again, good tutorial mr. ;D

[0112471324]

While the distinction between rational and irrational numbers if fascinating for historical reasons, I personally find the distinction between algebraic and non-algebraic numbers (transcendental numbers) to be even more interesting for theoretical purposes (especially in the area of uncountable sets). Do you talk about them in one of your videos? Anyhow, interesting video and a good introduction.

[chychochycho]

I don't have any videos done on sets yet. I'm still a ways away from doing a series on this. I need to get a few more things covered before opening up this can of worms, and I hadn't thought about doing a video on algebraic and transcendental numbers... great idea though. I'll have to think about this quite a bit before tackling it, but for the record, I do find the challenge of creating videos on this tempting. Thanks for recommending it.

[MAJESTIcag7]

In regards to the Rational Numbers.....how can they be Repeating or Terminating when those two words have opposite meanings?

Please explain if possible....

I'm 39 and have never understood math but have decided to truly apply myself and gain understanding and am finding your vids very informative so far...just to let ya know.

MAJESTIC

[chychochycho]

This should help. There are three types of numbers in the Real Number Set; terminating, ones that go one forever and repeat, and ones that go on for ever but never repeat. The first two are rational numbers (Q), and the third ones are called irrational numbers.

does that help?

[MAJESTIcag7]

@chychochycho Actually yeah it does...thanks!!!

[Entertainmentwf]

I like this video but I wanted to point out something. any integer divided by 0 is not defined. Division by definition is a divided by where b does not equal 0. It's impossible by the axioms of divisibility to divide by 0. Modulo arithmetic is the handy tool which helps get around this. But, I think you possibly confused this with approaching a division by 0 which is infinity or negative infinity typically (of the form lim n-> 0 k/n = +/- infinity) where k is a real number. :)

[chychochycho]

Thanks for pointing it out and you're correct. I'll be dealing with limits some time in the future, maybe even this year as a teaser. This video was just meant to be a quick intro to the Real Number Set without going into the specifics. As you know, zero and infinity are rather tricky to deal with :)

[robertlewisvazquez]

One of the best math video's I ever seen. Great job and thank you.

[chychochycho]

:-)

[johnrobieagain]

Thank you for your series.

I may contribute one idea in terms of rational numbers as you stated, they are fractions of Integer numbers (denominator mustn't equal 0).

Maybe it is better to define them as fractions with the numerator being a whole number and the denominator being a natural number.

Whenever "negative" occurs it can be attributed to the numerator.

Do you agree?

Thanks

Greetings from Germany

[chychochycho]

I like it :)

To simplify it though i would say, numerator is an integer and denominator a natural number. That way you don't even have to worry about explaining the "negative" part.

That being said, we should keep in mind restrictions (denominator can't = zero) when we start dealing with functions, since restrictions reveal a lot about the system we may be modeling.

[sydneyroxy]

Wow! this is crazy i have a picture of the wall behind you in my living room. Like that exact wall with the bench and everything my mom took the picture when she was in Cuba is it the same wall?

[chychochycho]

Nope, not the same wall. This is in Vancouver, however, i do hope to go to Cuba and do a series there in the future. I've been there a few times and absolutely love the architecture... there are some seriously beautiful walls there :)

[leoanderson3]

titties are good

[maxamed1985]

it was an arab guy who come up with zero and algebra was from arabia not iran,.

[chychochycho]

I think zero came from India. From wiki "The concept of zero as a number and not merely a symbol for separation is attributed to India" ... would be nice to get a confirmation.

As for algebra, yap, looks like Babylon (Middle East/Arab).

[imacheese1]

i thought 1/0 was undefined? not infinity.

[chychochycho]

1/0 is undefined. I was using the word infinity loosely.

[seemangal123]

water comes to my eyes.

[ssech6]

man i wish you had been mi teacher when i was small thanks for your videos very interesting 5 stars for you!!!!

[drexlfoley]

Please get a better source for sound!

[chychochycho]

as soon as i can afford an update I will.

[drexlfoley]

Cool, I havn't looked at all your videos yet, do you give intro to real analysis?

[chychochycho]

I haven't gotten into real analysis yet, or any analysis for that matter. I do however plan on introducing the concept of asymptotes when i get into zero and infinity and after that i plan on doing an intro on functions which should kick things into gear for analysis.

[drexlfoley]

Also sound source is Ok, when I posted that didnt realise you were outside.

[GR1o6180339887498948]

You've got few things wrong here. Rational numbers were known since the time of the Egyptians and were understood fairly well (do a research on Papyrus Rhind and Moscow Papyrus) although they reduced all fractions do additions of fractions with 1 as the numerator. Greeks discovered the irrationals only because they understood the rationals, 0 was found next by the Indians or the Chinese and then came the negatives; much later we get the complex numbers :)

[chychochycho]

cool, i'll have to look into the details of the history some time ... right now though, it's how to speak the language that matters.

[luisfigo7et10]

It is scandalous, a part of what is said is false and another part with a very bad and awful view.

For everyone if you really want to learn about maths, and know what truely is, and that there is certainly not mystery about, go to school or/and read books.

This man must improve his acknowledge about maths. And start to separate maths which is a model and the real world, and have a very well view when they join.

If i had the time i would have make a video.

[MAJESTIcag7]

@luisfigo7et10 And you're busy doing what exactly?

[eryksun]

luisfigo7et10, axiomatic set theory (ZFC) is useful, but it is surrounded by problems and controversy: the axiom of choice vs determinacy, the continuum hypothesis, the axiom of constructibility, transfinite cardinals, the Banach-Tarski paradox, etc. The various schools of thought are almost religious.

[miguelcotto4ever]

what type of math would nuclear physics use?

[luisfigo7et10]

the continuum hypothesis is not a problem because it is proved that with or without this set, there is no difference for the theory. Axiom of choice, is just an axiom one more, as 1+1=2, and is very natural like this one. So no problem, it's the same with the others.

It's only mathematical objects and logic, they don't exist in the real world.

It is not religion at all !!

If you were mathematician and have a religion and faith, you ought to know this.

[helgihg]

Somehow I feel like this video taught me more than an entire semester in high school.

[miguelcotto4ever]

teachers arent payed to teach. they are payed to vote for there union reps!

[luisfigo7et10]

Horrible! numbers are built with axioms, there's is no mystery with 0 it is only the cardinal of the emptyset.

Don't make the confusion between the writing system for counting and N which was built by axioms there's a big diference.

there's nothing mysterious about 0, it is highly regreatable to make this for the people.

[miguelcotto4ever]

what is the point of set theory? I mean do engineers use it for jet propulsion or for making a better computer? Does it offer any benefit to engineering or science?

[luisfigo7et10]

Yes absolutly, in all computers and programs it is used set theory, and now with new and few known langages we have program for each axiom including axiom choice, and that can make program without errors which is almost never the case. Here you are.

[luisfigo7et10]

PS: it is a response for miguelcotto4ever

[babuy1995]

I think those guys he was talking about are so addicted to sheeps, its kind of a funny though.....hehehehehe

[babuy1995]

Hi, Sir...Ummm I'm a kid. And here we have High School, no grades 7,8,9 or whatever.. Our teacher told us to look for a book with "The Real Numbers" in the library. But unfortunately...I forgot..hehe. So I searched the web and found one on youtube that sounds nice b'cause its a vid. which makes me easier to understand than reading. So I watched it and found out that this guy should be on an educational TV channel. What I meant was thanks dude, your so kind helping kids like me, any way..its nice

[dizzytrizzy07]

@babuy1995 hi babuy ;) born in the '95 ka no.. year of the pig.. kaya babuy :D hehe. Dizzy Trizzy here. my pinsan studies in ateneo de davao too ;3 kaso college na sia :)

[jdmspecracing]

simply amazing

[system0slaven]

Thanks

IM learning english and math Thanks

[ViolentVibrato]

Awesome videos, this is a brilliant, brilliant learning tool! Your engaging, informative, and everything flows.

[chychochycho]

:-)