Pre-Algebra 33 - Real Numbers

There are an infinite number of rational numbers, but there are infinitely more irrational numbers. Neither type of number can represent every type of numeric quantity. By combining the rational and irrational numbers into the real numbers, a continuum of numbers is created which can represent any quantity in the real world.

[invalid]

I was an original student of your series, years ago I don't remember.

I studied this during ninth grade as a means to consolidate my knowledge. I am now going to go to university for Engineering.

Great series. Would recommend to anyone, despite their math knowledge. Foundations are important.

[Gymomanen]

Haha, I really enjoyed this collection of movies. To be honest, I was sitting about 5 hours straight watching the whole playlist of videos. Really, the 12th of April is my birthday, and I kind of celebrated my 16th birthday watching these well thought out and educational series. Thank you for the present. May the mathematics live on into the infinity! (Literally)

[tatsumakisempyukaku]

I watched and took notes on all 33 lectures just so that I can get to the bottom of what was the character, Theaetetus, in Plato’s book “Theaetetus”.

In the book Plato is asking abojt what is the Is-ness of knowledge.
And Theaetetus says there’s a knowledge of making x or of y, or if z or of p and so on and so forth.
Socrates didn’t like the answer. He wanted a definition of knowledge that would encapsulate them all.

Then Theaetetus gave the reason why he was likely thinking this way and starting talking about the roots of 3 or 5 and how they were incommensurable.

My math was fuzzy. Haven’t done a lot of it in years. Did calculus in college like 22 years ago and I did nothing even close to that for years. So I was very rusty on many rules to say the least.

But I see why theaetetus was using roots to talk about how knowledge appears.

[azhun]

So interesting and useful!!! Real knowledge in this world. Thank you so much!!! Me:☺️😚😘❤️❤️❤️ You:🥰

[techcorp]

Great work..Please make this pre-algebra series an infinite one too...

[ValeriaFranco]

I loved these 33 lessons! Thanks so much for creating them!!! Please could you give us some link where we can find exercises to make practise?

[asifs]

OMG, that final statement in the whole series was so brilliant! I was actually just sitting alone laughing out loud...🤣

[kantaprasadsinha]

Excellent. Want to hear from Professor, how cabalistic ideas of Pythagorean were derobed . Did Pythagorean including Exodus took serious path to explain geometry based number theory to deify Pythagoras ?. Did Archimedes break the chain . Kindly explain. KPSinha from India.

[lrpbpb]

A "countable" infinity simply means that it can be represented. The number line can define all integers, though you don't (and can't) write them all, so you use arrows to indicate the line extends indefinitley. Similarly, a table can be used to logically represent all rational numbers. However, there is no system that could define all irrationals, beyond saying there are an infinite number, so they are uncountable infinity. Since the reals contain irrationals, they also can't all be represented.

[StationMy]

How can real number be an as big infinty as irrational numbers since real number are rational numbers and irrational numbers combined ? This will mean that you real number infinity will always be a countable infinity bigger than the irrational numbers.

[ericnovaktube]

If Rationals aren't continuous because we can slip roots in the gaps, neither are Reals when we slip Infinitesimals in from the Hyperreals essentially creating gaps.

[interestelar]

Congratulations!!! Great Video, also if you understand math this video help to get more...

[infinityhypercubed]

For those of you who are arguing that the numbers on the line take up zero space and therefore can't exist, that is simply not true. Imagine every number taking something like 1/<><> of the line, so it is always at least one infinitith bigger than 0. So, no, this can be true because 1/<><> is greater than 0, even though it is infinitely small.

[hasanalj]

can any real number be expressed as square root of a rational number?

[farahjaber]

you said in a lecture about roots that there's no square root of a negative number;so is it because there not real

[svommams]

If your head is not about to explode after watching this, then go read about the surreal numbers.

[sasmas]

Yes, and they are equally infinite as real numbers, therefor "uncountable." They're known as imaginary numbers.

[flance]

Thanks for answer. You're great!)

[MegaMementoMori]

integers = (natural numbers x 2) + 1.

Rational numbers = integers x infinity.

Real numbers = rational numbers x infinity.

So that means that real numbers = integers x infinity squared...

in other words the square root of real numbers is infinity x the square root of integers...! (head explodes)
... not to mention that this infinity can be either positive or negative!!!

[hasanalj]

becouse Real numbers and Irrational numbers are both same type of infinity (uncountable). and infinity + infinity = infinity.