Welcome To Hyperreal Numbers! | Number Theory

[@Garfield_Minecraft]

OwOmega 8:54 so they are way too real to even be real. **hyperreal** , you can technically count to omega then backward again in finite amount of time just do supertask god can totally do that it doesn't take long this comment wasn't meant to be serious so.. yeah was having fun learning math and counting in term of infinity

[@manicmath3557]

@@Garfield_Minecraft HAHAHA thats really clever love the supertask joke HAHAH

[@sruthisruthi3906]

Well done! Excited to see more from you 😊

[@raifegeozay687]

there is also things like epsilon^2 it is other number line that is infinitely squished the infinitesimal line. in the same way you can have epsilon^3,epsilon^4 or even epsilon^omega (and its variants) or omega^2, omega^3,..., omega^omega,..., omega^omega^omega,...,omega^omega^omega^omega^... omega times (and of course its variants) and also uncountable infinitely big or uncountable infinitely small (and its variants)

[@manicmath3557]

Infinity isnt a nimber. When i said epsilon is one over infinity. I meant one over omega. Since okega is a proper way to denote infinite amount as a value

[@ma.luvimmacabale6951]

Great job!

[@manicmath3557]

Dont do a drinking game for evert time i say 0 or you will definitely die of alchohol poisoning.

[@rafaris2230]

Great job, Joshua!

[@tomassajor6326]

We’re so PROUD of you Josh!!!🙂

[@idettax66]

Hey I really like the quality and the confidence you display in this video! But I just want to clarify some stuff. You said that you can get things like omega +1 and absolon / 2. Since they are both the largest and smallest numbers respectively, does that mean that if you do anything to those numbers using basic functions like plus, minus and all that, it will always equal to itself? As in omega + 1 = omega.

[@manicmath3557]

Hello thanks for the feedback. I think my freezing was quite misleading when I said Epsilon was the smallest and Omega was the biggest. The thing is you can have number is smaller than Epsilon by halving Epsilon, or you can have something after than omega like omega plus 1. Omega isnt the biggest hyperreal. Its bigger than all the reals. But you can have hyperreals more or less than omega. And epsilon is smaller than all reals. But you can have hyperreals more or less than epsilon. Its just that if i had all the reals plus omega. Omega would be biggest in the bunch. But i can have bigger hyperreals than omega Also side note. omega plus 1 isnt actually bigger than omega. This is quite confusing but I will explain more when I talk about Cardinals and ordinals in another video. Omega isnt really a size but a position. So its not really that omega is big. Its that omega in terms of position cones after all the infinite real numhers. This sidenote is confusing but I will elaborate when I talk about it in the future Thank you so much for your feedback, I am not actually very confident in my speaking so this is nice to hear that I may be improving thank you for watching and have a great day

[@idettax66]

@@manicmath3557 oh I think I understand where you’re coming from. Although the concept of hyper reals are completely new to me, I have learnt about countable and uncountable infinities. So I guess it’s somewhat similar to this?

[@manicmath3557]

@@idettax66 yes thats kinda the idea. Vsauce made a video called How to count past infinity. Its so fun and great in explaining this concept. Also how omega plus one is technically not bigger than omega Here kzbin.info/www/bejne/iaO4aox6pL14bpo

[@klaraaviete9148]

would -w (omega) be a hyperreal number? great video, thanks:)

[@manicmath3557]

Oh yes! Hyperreals are just an extension of the reals and act like how real numbers work in algebra so you can of course have negatives!

[@Alice-to3wj]

Well done!

[@mchikos]

This is great!

[@manicmath3557]

Thanks!

[@tmlawson751]

Been trying to make sense of 'hypernormal' in mathematics to connect it with interdisciplinary subject. So far the closest thing that's written about it is in relation to hyperreal numbers. I understand neither!!!! XD but this is a great video.

[@Joshua-qm1hc]

good job 👍