Learn more about scienceandnature with this collection

The historical significance of urban centers

The impact of cultural and technological advances

The role of urban centers in shaping society

How can, according to George Cantor’s version, formally determine that there is an infinite series of numbers that is more infinite than another infinite?

Simply by making a relationship (connecting in) between each member of the two sets.

So, if the members of the two sets can be connected one to one (bijective), then it means that they are the same amount of number, both have the same amount of infinite.

Put simply: there is an infinity that is shorter than another infinity. You see, this reasoning is much more absurd, but forcing it, as this is a mathematical structure.

17

110 reads

MORE IDEAS ON THIS

Surprisingly George Cantor claims there is an infinite-2 which is greater than infinity-1.

Isn’t infinity enough innumerable? Then how can there be two kinds of infinite, where one "infinity" is greater than the second "infinity".

Yet intuitively, the infinite is pretty much weird. ...

19

202 reads

Those all sets are just one set of infinite number, and we did arranging those numbers into different set of point of view, so we thought we were dealing with something different increasingly at different stage of infniity.

It’s just a set. Only they did interchange in between numbers, so i...

15

53 reads

What is the method for measuring that something that is innumerable can challenge another that is also innumerable?

I will give an example before going into the formal method, so that we can see the weird of the continuum hypothesis in this case.

It’s like between hot water & ice wa...

17

128 reads

When you point to the number one, you are actually pointing to something that exists.

The question is "how wide is the “number 1" you’re pointing at?"

- ... Of course the number 1 is the area of 0 to 0.999999999999999 ...
- ...Similarly the number 2 is

area from 0 to ...

17

63 reads

You have to relate math on reality. if you reject this, try with small step. consider a number must be related to a thing, otherwise we're dealing with nonsense. although someday someone accept math explaining other dimention, or relativity, still it has to do with things. there is nothing simple...

10

37 reads

A series of numbers is always uncountable, so how can there be a series of numbers that is more uncountable than the one that was previously uncountable?

How to measure one thing than the other when both are equal? Thus the method was found which became the root of this problem. Some have o...

18

172 reads

1

❌

2

❌

3

❌

4

❌

5

They thought there were points that couldn’t be connected (marked by a red cross) one to one (bijective) from left to right (from the member of the...

17

62 reads

Actually, whether we are trying to do cantor’s diagonal, or multiplying power set of aleph-null, but it’s actually we are doing on the same numbers as whole numbers, as one infinity.

Although you can create multiple infinities, still we are doing on the same range.

- It’s just that...

14

50 reads

I’m focusing on “overlap”. Cantors diagonal numbers don’t overlap with the ones on the list either. Even and don’t overlap odd either. Since we can order {0,1,3..} and {0,1,2,3,4…} by the time we get to 2 in the second list, we know we will never find it in the first. Both are infinite yet differ...

11

24 reads

The Concept of Infinity in the Continuum Hypothesis

This is not as commonly known, infinite value. But countless in different contexts.

However, the sequence of numbers of any type is always infinite, in the sense it's unreachable.

There are two infinite series of numbers, th...

19

377 reads

It’s like when we button a shirt, so if all buttons are buttoned, it is assumed that the left and right sides are the same length.

But when the buttons don’t fit properly, so you can see that there is a longer side of the shirt. But actually THE LEFT SIDE & RIGHT SIDE IS TOTALLY THE SAME LE...

17

114 reads

So that between the members of the set of integers and the members of the set of real numbers (involving decimals), it can always be paired (connected) one to one (bijective) for all members of the two set of different types of numbers.

This also has confirmed that from the left side to the...

17

69 reads

A single finite number may be related to a banana. two finite numbers may be related to two bananas. more & more numbers may be related to more and more bananas, rocks, books, atom, and so forth. more & more infinites number then, must be related to all of possible things that fill the entire pos...

10

39 reads

Continuum hypothesis is failed, because of these reasons:

If we can do multiple calc on different areas of infinity and that looks like we are doing things differently, or we're dealing with different infinity, but actually we're doing at the same area, the same numbes were used interchange...

13

39 reads

What are the useful outcomes of denying the Continuum Hypothesis?

This opens new perspective of how we think on math.

_____

How do the integers and ...

10

46 reads

Related collections

More like this

What are the useful outcomes of denying the Continuum Hypothesis?

This opens new perspective of how we think on math.

_____

How do the integers and ...

Generally, no part of your brain is exclusively dedicated to creativity or mathematical reasoning. **Neurons compute every action you take from across the entire brain.**

While your cerebral cortex consists of two halves, both are intricately connected. Language ability does t...

Continuum hypothesis is failed, because of these reasons:

If we can do multiple calc on different areas of infinity and that looks like we are doing things differently, or we're dealing with different infinity, but actually we're doing at the same area, the same numbes were used interchange...

Explore the World’s

Best Ideas

Save ideas for later reading, for personalized stashes, or for remembering it later.

Start

31 ideas

Start

44 ideas

# Personal Growth

Take Your Ideas

Anywhere

Just press play and we take care of the words.

No Internet access? No problem. Within the mobile app, all your ideas are available, even when offline.

Ideas for your next work project? Quotes that inspire you? Put them in the right place so you never lose them.

Start

47 ideas

Start

75 ideas

My Stashes

Join

2 Million Stashers

4.8

5,740 Reviews

App Store

4.7

72,690 Reviews

Google Play

Sean Green

Great interesting short snippets of informative articles. Highly recommended to anyone who loves information and lacks patience.

“

Ashley Anthony

This app is LOADED with RELEVANT, HELPFUL, AND EDUCATIONAL material. It is creatively intellectual, yet minimal enough to not overstimulate and create a learning block. I am exceptionally impressed with this app!

“

Shankul Varada

Best app ever! You heard it right. This app has helped me get back on my quest to get things done while equipping myself with knowledge everyday.

“

samz905

Don’t look further if you love learning new things. A refreshing concept that provides quick ideas for busy thought leaders.

“

Ghazala Begum

Even five minutes a day will improve your thinking. I've come across new ideas and learnt to improve existing ways to become more motivated, confident and happier.

“

Giovanna Scalzone

Brilliant. It feels fresh and encouraging. So many interesting pieces of information that are just enough to absorb and apply. So happy I found this.

“

Jamyson Haug

Great for quick bits of information and interesting ideas around whatever topics you are interested in. Visually, it looks great as well.

“

Laetitia Berton

I have only been using it for a few days now, but I have found answers to questions I had never consciously formulated, or to problems I face everyday at work or at home. I wish I had found this earlier, highly recommended!

“

Read & Learn

20x Faster

without

deep**stash**

with

deep**stash**

with

deep**stash**

Access to 200,000+ ideas

—

Access to the mobile app

—

Unlimited idea saving & library

—

—

Unlimited history

—

—

Unlimited listening to ideas

—

—

Downloading & offline access

—

—

Personalized recommendations

—

—

Supercharge your mind with one idea per day

Enter your email and spend 1 minute every day to learn something new.

I agree to receive email updates