@design_RG
Was thinking about taking Quantum Physics lesson from YT after the semester. The subject always seemed baffling.
@Surasanji

@shibaprasad @design_RG Well, this is a math thing. I'm not sure how/if it would apply to Quantum Physics.

@Surasanji @shibaprasad Yes, true, it's just another example of concepts that are difficult to understand and accept. Einstein apparently had a hard time accepting Quantum theory too, I find that comforting.

@Surasanji
Yeah I know. @design_RG said about Quantum so I said that.

@shibaprasad @Surasanji

My bad, took thread on a tangent. Sorry. 😏

Now back on the Math side, is it a fact, what you mentioned? Are there bigger and smaller infinities?

@design_RG @shibaprasad Yes. You'd think based on the concept of infinity they'd all be the 'same size'. This is apparently not true. You can have infinities that are more or less infinity than another infinity.

@Surasanji @shibaprasad *heads out for research*

https://www.bing.com/search?q=bigger+or+smaller+infinties

@design_RG @Surasanji Yeah there is. Actually for most cases, infinity is a concept which denotes a high value. Not a particular number. I can give a small example:

Suppose in a Graph you have two sqaures formed with x=0, y=0. In them the length of one is 5*5 and another is 10*10.

Now for 5*5, you can have infinite numbers of points inside the, Similarly for 10*10 you have that. But as you can imagine the number for 10*10 will be much larger than 5*5. And both are infinite!

@design_RG @Surasanji inside the square*

@shibaprasad @Surasanji Physically, I can graps the concept, the 10 x 10 square has four times the area of the 5 x 5 one.

But really? until now I have thought that the number of points is infinite in both cases, and wouldn't be quantifiable as in, one has more than the other.

@shibaprasad

You won't regret it!

@design_RG @Surasanji

@freemo @Surasanji
The infinitely big and the infinitely small are infinitely related

@Karthikdeva @freemo @Surasanji

I just finished reading (and then re-reading, up and down) an excellent article.

https://cosmosmagazine.com/mathematics/some-infinities-are-bigger-than-others

Until about halfway into the article I felt my previous belief on sets being not comparable, not larger or smaller if both are infinite.

"It is tempting to say there are twice as many natural numbers as even numbers. But that’s wrong.

When we say two sets of objects are equal, we put them into correspondence on a one-by-one basis. For example, if I claim I have the same number of fingers as toes, I mean that for every one finger there corresponds one toe, with no toes left over and no fingers left unmatched at the finish.

Now do the same for natural numbers and even numbers: pair 1 with 2, 2 with 4, 3 with 6, and so on. There will be exactly one even number for every natural number. The fact that each series forms an infinite set means the sets of numbers are the same size, even though one set is contained within the other! "

Aha, I thought!! 😃

But... Read on...

"This is best understood by envisaging a continuous line, labelled by equally spaced natural numbers: 1, 2, 3 and so on. There will be an infinite number of points between 1 and 2, for example, with each point corresponding to a decimal number. No matter how small an interval on that line and how much you magnify it, there will still be an infinite number of points corresponding to an infinite number of decimals.

It turns out that the set of all points on a continuous line is a bigger infinity than the natural numbers; mathematicians say there is an uncountably infinite number of points on the line (and in three-dimensional space). You simply can’t match up each point on the line with the natural numbers in a one-to-one correspondence. "

So, the Learn New Thing of the Day is that there ARE sizes of infinities. Owa. 😲

By all means read the article --- it's NOT hard to follow, really well explained and authored by a Uni professor.