What is the answer you can get when you take infinity in solving the problem of mathematics?

Answer 1

For every number, you have one point. For every point, you have one number. So there is one to one correspondence between number and point on the number line. Let us see the number of points between 0 and 1. Between 0 and 1, you have 1/2. Between 1/2 and 1, there is 3/4. Between 3/4 and one you have 7/8. Between 7/8 and 1, you have 15/16. So between any two given points, there are infinite points. That means there are 'infinite points' between 0 and 1. Statement (X).

By the same logic, you can prove that there are 'infinite points' between 0 and 2. Statement (Y).

Now from statements (X) and (Y), X = Y.

So 1 = 2.

This way you can prove that any number is equal to any another number.

Alternately You can cut line segment of the length 1 out of the number line. You can do it infinite times. Statement (X).

You cut the line segment of the length 2 out of the number line. You can do it infinite times. Statement (Y).

You can cut the line segment at the length of million, billion or trillion each. Still you can do it infinite times. (Z)

From statements X and Y, 1 = 2.

From statements X and Z, 1 is equal to million, billion or trillion. (What ever you take the value.)

You can take any other numbers instead of 1 and 2 and prove that they are equal.

It is logical that when you cut the pieces of the "size" 1, as compared to the "size" 2, You will get double number of pieces of "size" 1 as compared to the "size" 2.

But both will be "infinite".

Then you may have to say "infinite (1)". Then "infinite (2), "infinite (3) and like......"infinite (infinite). So there will infinite "sizes" of infinite. Nowhere in past the "size" of the infinite is mentioned or considered. The fact is that all the numbers are "same" as compared to infinite. Because there is on such number called as "infinite".

The moral of the story is that you do not know what infinity is! The fact is that human brain can not understand the "actual" concept of infinity. The fact is that everybody "says and presume" that he knows the concept of infinity. It takes little knowledge to know that you do not know anything. Only great philosopher Socrates had that knowledge, in the history of mankind.

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So do not take infinity symbol in your mathematical calculation to prove anything. When you take multiple steps in a circular logic, it is almost impossible to find the fault.

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(By the way the concept of infinity is mentioned in almost all the Holy books. I did not read the Holy Quran. But my Muslim friend told me that it is mentioned that you take the ink equal to all the seas on earth and write about the God (Allah). All the ink will be finished but then the description of God will not be complete. The same concept is repeatedly mentioned in Bhagwadgita also. (That is the holy book of Hindus.) I did not read the Holy Bible. But I am sure that the same concept has to be there and that too, repeatedly. The same concept has to be there in the Holy book of Judaism. All the souls are nothing and of "same size" as compared to that "Infinite God".)

Answer 2

The answer depends on the context in which infinity crops up. Not only that, but it can also depend on the "size" of the infinity: countably infinite (eg number of rational numbers) or uncountably infinite (number of real numbers).