Thread: Infinity query

Not being bothered about how big infinity is , can following doubts be cleared ?


If difference between zero and one is one ,
Is it possible that , the difference between (infinity/2) and its next number is also ONE.

Infinity is not a real number and cannot be used as one, so the question makes no sense (nor does the successor of infinity).

The first infinity is the number of integers.

The next infinity(*) is the number of reals. This is infinitely larger than the first infinity.


(*) Probably. This has not been proved.

series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .

1-2 =-1
2-1 =1

(x/2)-((x/2) + 1) = ?


((x/2)-1) - (x/2) = ?

Originally Posted by sciencestudy

series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .

Yes, because that is how the natural numbers are defined.

(x/2)-((x/2) + 1) = ?

= ((x/2) - (x/2)) - 1 = -1 [Edit: corrected sign]

((x/2)-1) - (x/2) = ?

= (x/2) - 1 - (x/2) = ((x/2) - (x/2)) -1 = -1

So, what is your point?

Originally Posted by Strange

Originally Posted by sciencestudy

series of numbers from 1,2,3,4...................x , difference between each is one. no infinity. X is finite .

Yes, because that is how the natural numbers are defined.

(x/2)-((x/2) + 1) = ?

= ((x/2) - (x/2)) + 1 = 1

((x/2)-1) - (x/2) = ?

= (x/2) - 1 - (x/2) = ((x/2) - (x/2)) - 1 = -1

So, what is your point?

If ((x/2)-((x/2) + 1) = ?
= ((x/2) - (x/2)) + 1 = 1= (x/2) - 1 - (x/2) = ((x/2) - (x/2)) - 1 = -1

So , what is (( x/4)-((x/4)+1)= ?
(( x/4)-((x/4)-1) = ?
do you have any idea , what's going on here ?

Originally Posted by sciencestudy

So , what is (( x/4)-((x/4)+1)= ?

-1

(( x/4)-((x/4)-1) = ?

1

do you have any idea , what's going on here ?

Yup.
You have no idea of mathematics.

Originally Posted by sciencestudy

So , what is (( x/4)-((x/4)+1)= ?

n - (n + 1) = (n - n) - 1 = -1

For all values of n (x/2, x/4, etc.)

(( x/4)-((x/4)-1) = ?

n - (n - 1) = (n - n) + 1 = 1

For all values of n (x/2, x/4, etc.)

do you have any idea , what's going on here ?

I have no idea what you think the problem is. This is basic arithmetic. (Although, embarrassingly, I got the signs wrong in the previous post ... )

Just to throw a spanner in the works , for a conditionally convergent infinite series such as:



rearranging the terms can alter the sum.

Originally Posted by KJW

Just to throw a spanner in the works , for a conditionally convergent infinite series such as:



rearranging the terms can alter the sum.

Thanks for making me relive an embarrassing moment from an undergraduate maths class, where I got this wrong on an exam. The series was presented in a re-arranged form. I re-re-arranged it into the form above, thinking that I was terribly clever to have done so, and wrote down "the" answer by inspection.

I cringe whenever I recall it. Thanks a lot.