# Infinity has an end..

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If you can parse this sentence

3 hours ago, CuriosOne said:

Do the numbers "going up" or going "down" "travel" towards infinity towards that 0 in the center??

you're a better man than I am, Studiot.

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23 minutes ago, studiot said:

Well I think this is a perfectly reasonable question and a good one to discuss.

Also I think this is much better put than recent posts (though I would have liked the picture the right way round).

+1 for encouragement to do more of this and start wiping out those red ones.

Perhaps you will notice that there are actually two (or is it three with the negatives) infinities going one here.

There are the numbers being suqred, which are increasing one at a time

0,1,2,3...

and there are the squares themselves

0,1,4,9...

Which are increasing much quickly.

I'm glad I posted this as i seldom pay attention to the "y part" I have to admit,  because I'm under the impression the y part is + up all the time since time is always positive.

Which "prematuraliy" aimes my focus to the negative numbers doing something 'exponentially'  to the symetry of:

y=  x^= -1

""""Not sure if it's written like that""""

"What causes this symmetry?

""More on that later""

But why would I think this??

"In My Visual Opinion And Logic At Theses Higher Dimension Of Geometry."

The increasing values of x and the squared values of y appear to geometrically "visually" look like a perfect trangulized " or rendered" flat square in infinite directions of 3×2 for a "6 sided hyper cube"..But maybe that's pushing it, but its intresting to think it may look like this..

Again, I get this "idea" from:

negative numbers doing something 'exponentially'  to the symetry of x = -1....

IE The 3rd dimension...

I cannot fully put my insight on this, untill I understand without failure more on this subject...

44 minutes ago, MigL said:

If you can parse this sentence

you're a better man than I am, Studiot.

Or left and right, or +, - directions, the calculator input goes up or down via the up, down arrows on my calculator...

I should have re-phrased that.

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On 11/9/2020 at 10:43 PM, CuriosOne said:

Both bugs and stakes, I don't understand why you mention them...Seriously what do those have todo with infinity??

It was a quick example* of a context where discussing "the last number before infinity" actually makes sense. Feel free to ignore the example (it was mainly intended for Migl) if you do not like it.

*) based on experiences. I also note that my misspelling of "stakeholders" made the example unnecessary sketchy.

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17 hours ago, MigL said:

This is an example of an improperly posed question.
Approaching infinity or approaching zero ?

How are we to make out what you actually wish to ask ?
Come-on, you can do better.

These are "informal" questions for now..

It may make sense later..

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21 hours ago, MigL said:

This is an example of an improperly posed question.
Approaching infinity or approaching zero ?

How are we to make out what you actually wish to ask ?
Come-on, you can do better.

Didn't you say infinity was not a number and infinity does not follow one??

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2 hours ago, CuriosOne said:

Didn't you say infinity was not a number and infinity does not follow one??

That is correct.
Infinity does NOT act like a number
infinity + 1 = infinity
Infinity - 1 = infinity
And for that matter, infinity +/- ((((((10)^10)^10)^10)^10)^10) …  is still equal to infinity.
What other number has those properties ??

What is the last number before infinity ?

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6 hours ago, MigL said:

That is correct.
Infinity does NOT act like a number
infinity + 1 = infinity
Infinity - 1 = infinity
And for that matter, infinity +/- ((((((10)^10)^10)^10)^10)^10) …  is still equal to infinity.
What other number has those properties ??

What is the last number before infinity ?

A number without + or minus - I suppose...I'm still pondering on the list question..

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On 11/11/2020 at 11:27 PM, CuriosOne said:

I'm glad I posted this as i seldom pay attention to the "y part" I have to admit,  because I'm under the impression the y part is + up all the time since time is always positive.

Which "prematuraliy" aimes my focus to the negative numbers doing something 'exponentially'  to the symetry of:

y=  x^= -1

""""Not sure if it's written like that""""

"What causes this symmetry?

""More on that later""

But why would I think this??

"In My Visual Opinion And Logic At Theses Higher Dimension Of Geometry."

The increasing values of x and the squared values of y appear to geometrically "visually" look like a perfect trangulized " or rendered" flat square in infinite directions of 3×2 for a "6 sided hyper cube"..But maybe that's pushing it, but its intresting to think it may look like this..

Again, I get this "idea" from:

negative numbers doing something 'exponentially'  to the symetry of x = -1....

IE The 3rd dimension...

I cannot fully put my insight on this, untill I understand without failure more on this subject...

I presume this was an answer to my question

On 11/11/2020 at 10:33 PM, studiot said:

There are the numbers being suqred, which are increasing one at a time

0,1,2,3...

and there are the squares themselves

0,1,4,9...

Which are increasing much quickly.

$\begin{array}{*{20}{c}} 1 \hfill & 2 \hfill & 3 \hfill & 4 \hfill & 5 \hfill \\ 1 \hfill & 4 \hfill & 9 \hfill & {16} \hfill & {25} \hfill \\ \end{array}$

1. The top row is made up of the natural counting numbers.
So the count of these numbers is the same as the largest number.
In my example there are 5 numbers in the top row and the count of numbers is also 5.

2. In the second row which are simply the squares of these numbers, there are also 5 numbers
But the they are all larger than the corresponding number in the top row (except for the 1).

3. So whatever might be the largest number in the top row as it is extended, there is always a larger number in the bottom row.

4. This larger number is also a simple integer and so whatever number you propose as the 'end' number of of the top row is not the largest integer and not the end of the row.
That is the process of counting has no end. This is called a non terminating infinity.

5. It is also interesting to note that the bottom row does not include all the numbers in the top row; it does not contain 2,3 or 5 or other top row numbers if it is extended.

6. Yet for every top row number there is an entry in the bottom row so the count is the same in both top and bottom rows. There is the same count of numbers of the bottom row as for the top row. This property is called the cardinality. Cardinality is very important in comparing infinities.

7. This is a truly remarkable property of infinities.

It is important to stay focused with this stuff and not mind-hop to many disparate subjects.

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8 hours ago, studiot said:

I presume this was an answer to my question

112439416525

1. The top row is made up of the natural counting numbers.
So the count of these numbers is the same as the largest number.
In my example there are 5 numbers in the top row and the count of numbers is also 5.

2. In the second row which are simply the squares of these numbers, there are also 5 numbers
But the they are all larger than the corresponding number in the top row (except for the 1).

3. So whatever might be the largest number in the top row as it is extended, there is always a larger number in the bottom row.

4. This larger number is also a simple integer and so whatever number you propose as the 'end' number of of the top row is not the largest integer and not the end of the row.
That is the process of counting has no end. This is called a non terminating infinity.

5. It is also interesting to note that the bottom row does not include all the numbers in the top row; it does not contain 2,3 or 5 or other top row numbers if it is extended.

6. Yet for every top row number there is an entry in the bottom row so the count is the same in both top and bottom rows. There is the same count of numbers of the bottom row as for the top row. This property is called the cardinality. Cardinality is very important in comparing infinities.

7. This is a truly remarkable property of infinities.

It is important to stay focused with this stuff and not mind-hop to many disparate subjects.

That is quite "profound" and easy to understand...Thnx!

I literally "wrote" down specific notes from your reply, I will research Cardinality in extreme depth..

"I can see now why it is important to stay focused with this stuff.

There are other images along with the list of numbers i placed in this thread that id like to share in due time, for now i will learn Cardinalality and get back to this post ASAP.

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