Is infinity plus one bigger than infinity?

Question

think about it.

Answer 1

Doubtful.  Infinity goes on forever, so adding that one to forever just...ugh...I can't even explain that one...bravo!  

Answer 2

I think it is a bad question.  It seems similar to the question can God make a rock so big that he cannot lift it.  The answer creates a false delimma given the concepts involved.  God can make an infinitely big Rock and God can lift an infinitely big rock.  Infinity plus one is nothing more than infinity again.  It is a bad question.

Answer 3

No, by definition.

(It is only bigger on 3rd grade playgrounds)

Answer 4

In your scenario, no.  The line can't be added to, because there is no place to add to.  The line would just overlap the line segment.

EDIT:  ***This is the second time I've revised this answer, but let me try again, because I think this is an important question.

Technically, infinity is an unbounded, limitless quantity.  1 is a finite quantity.  The problem with your question is an error of language.  In your question, you've implied that you intend to add to something that can't be added to, because there is no maximum limit to infinity.  In order to reconcile your question, you must either change what you mean by infinity, or what you mean by + 1.  Otherwise, the question isn't logical.

If you change the conditions of the quantities, it is possible to have two initially infinite quantities that aren't equal to each other under the new conditions.

For example, if two people start at one point and walk in the same direction forever, then they will each walk an infinite distance.  If one person has a head start of one mile, then that person will always be ahead of the second person by one mile.  In order to measure this difference in distance travelled, though, you have to reduce the time frame to a finite length, rather than keeping it set at "forever".

To Marc Hector:  What I was trying to point out in my example is the relative difference between the two quantities.  You can't say that infinity and infinity + 1 are equal to each other in all conditions, because under certain conditions, the dimensions of a quantity are only frames of reference.  I like your answer, though!

Answer 5

no beacause infinity is infinity and no matter what u add to it it will always be bigger

Answer 6

is human stupidity plus one other person's bigger than human stupidity? think about THIS.

Answer 7

No.

Answer 8

Infinity is similar if not equal to eternity, which has no beginning and no end, and therefore nothing can be added or subtracted from it.

Answer 9

yes.

The way I see it, think of infinity as counting, starting at one, but never ever stopping. Because infinity simply doesn't end, but it has to start somewhere, right?

But if someone else starts at two, (one plus one) and keeps counting and never stops, they will always be ahead. Therefore, even if the numbers never end, it will still be bigger.

Answer 10

In one of his earliest papers, Cantor proved that the set of real numbers is "more numerous" than the set of natural numbers; this showed, for the first time, that there exist infinite sets of different sizes. He was also the first to appreciate the importance of one-to-one correspondences (hereinafter denoted "1-to-1") in set theory. He used this concept to define finite and infinite sets, subdividing the latter into denumerable (or countably infinite) sets and uncountable sets (nondenumerable infinite sets).

Answer 11

It should be,   shouldn't it be?  That seems quite natural to me.  I heard adding one is the way to make anything bigger.  Just like another drop in the ocean!

But then I never was good at counting.  And I do wonder if all these wise people here know something that I don't.  I feel decidedly stupid...so I'll wait for your verdict...

Answer 12

Every number is grounded in the number 1. That is: 1, then you have 1+1, then 1+1+1, and so on.

If we add on the 1's forever, this will be called an 'infinity'. Since there is no end to the additions, there is no magnitude to infinity. Infinity is simply bigger than finite numbers, but that's it - that's all we can know - it does not have magnitude, but it contains all magnitudes.

Let me give you an example:

abcdefghijklmnopqrstuvwxyz

The above is the alphabet. It has no meaning. It is not a word. Yet all the words in the English language and all the semantics are contained in it. Infinity is very similar with numbers. It has no magnitude, no value, but all magnitudes and values are contained in it.

Now, whether we start at 1 or at 1+1, infinity is still infinity. For those who say a person who begins at 1 has more value that the person who starts at 2 (1+1) because they have an extra 1 have not grasped the true meaning of infinity.

Series A) 1+2+3+4+5+...

or

Series B) 2+3+4+5+...

Those people say that the first series is bigger. However, that is mathematically incorrect. See it this way:

Instead of 2 I will write 1+1 and instead of 3 I will write 1+1+1 and so on.

So, a new rendering of Series A would be:

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+...

and Series B:

1+1+1+1+1+1+1+1+1+1+1+1+1+1+...

Thus, you see that in the end, there is no difference. Why? Because the concept of infinity has no value. You can only add a value to 'another value'. But you can't add a value to something that has no magnitude or value such as infinity. Why doesn't it have a value? Because it goes on and on. Whenever you wish to determine a value for it, you have given it a limit, thus it won't be infinity anymore. The nature of the concept of infinity is not being able to give it a value, because values are properties of finite things.

The good thing about this question is that it's been posted in the Philosophy Section.

PS. As for the example of the man who is ahead due to the race with another man: first of all, the man will only be ahead if you ever stop the race - if you stop the race, you give it an end, you give it a limit, and it won't be infinity anymore. It will have a value.

Yet, the paradox here seems to be that when we follow the race until infinity, one man seems to be always ahead. Why is that?

This is because they will never ever reach infinity. If they ever did, that means there was a limit, therefore it wouldn't have been infinity.

So it is impossible for the race to go on until infinity because infinity is impossible to reach. Thus, every race would be finite NOT infinite. Therefore in every race, one man would always be ahead.

pps. As for the idea that an infinity can be 'more numerous' than the other, here's a little example:

Series C: 1+2+3+4+5+...

Series D: 1+3+5+7+9+...

Both series go on to infinity (which is impossible by nature). Yet C adds all natural numbers whereas D only adds the odd numbers. Yet, since infinity has no magnitude, there would be no difference between the two infinities.

However, the question is, how many numbers have been used in reaching this infinity in C and how many in D? We can safely say that in each segment of these two series, D is equal to 'half of C' since C includes both odd and even numbers. Yet, just like the race above, we can never ever reach infinity. That is why at any point, which is a limit, D will be 'half of C'. But if infinity is reached (which is impossible) then D will equal C (D=C).

So, whereas the two infinities are not different relative to one another, the finite segments that make up the infinities are.

Thus, the problem returns to our finite minds probing the concept of infinity.

Sorry if this has confused you, but paradoxes must be solved to clarify concepts and meanings.

Hope you enjoyed.

Answer 13

...no, infinity has no end...is still infinity...

Answer 14

Infinity is, by defintion, unreachable.  So, you cannot add one to it

Answer 15

Not really since Infinity is INFINITY. How the heck can you go more than forever? Infinity plus one would just be a figure of speech.