It's just a reductio paradox. X is the greatest number = infinite 1 can always be added to X X + 1, X1+ 1 etc.. Therefore, infinite can not be the greatest number...It contradicts itself and is self-defeating
But infinity is everything, infinity plus one is omething, therefore infinity includes infinity plus one...
infinity is not a number neither is banana adding 1 to banana is just as rediculous as adding 1 to infinity
Infinity is not a number its more of a concept. Something never equals infinity, it 'goes to infinity' is the usual phrase.
That's right, infinity is not a number, so infinity + 1 doesn't really make sense. However, you can talk about taking an infinite set and adding objects to it. For example, the set of natural numbers = {1,2,3,4,...} is (countably) infinite. And you can take that set and seamingly make it larger by adding 0 and get the whole numbers = {0,1,2,3,...}. But that new set is still just countably infinite. They are the same size (a set's size is called cardinality), even though one is clearly contained in the other. There are sets that are "larger" than countably infinite though, e.g. the set of all real numbers in uncountable, which is bigger.
god might have the answers. what would you rather do, ask him or become it? lucidcrous question really but what if there was a way how would you reckon that would be possible; to become a god, an avatar, a diety on earth.
So you take an infinite set and make it bigger. My set theory is very bad but aren't the natural numbers just a subset of the real numbers. So put another way your dividing an infinite number of elements by a number, which will of course still be infinity. This is based on the very poor assumption that infinity is a number to start with anyhow. My point being that if you treat infinity as a number is it perfectly possible to perform a function on it and still get infinity.
Well I'm definitely no set theorist either, but got a healthy dose of this in a topology class once. Yep, the natural numbers are a subset of the real numbers. And you're right that "infinity" is not a number in the sense that you can start doing arithmetic with. But it is a number in a way. In math there are objects called cardinal numbers. They are used to describe the cardinality, or size of a set. For finite sets, the cardinality is one of the natural numbers. So the first part of the cardinal numbers, the finite ones, are just the natural numbers: {0,1,2,3,4,...}. For example the cardinality of the set {2,4,6} is 3. But if you want to describe the size of the set of natural numbers you need something bigger than any of these. The first infinite cardinal number is Aleph_0, aka countably infinite. Any set that can be put into a one-to-one correspondance with the Natural numbers has cardinality Aleph_0. For instance, the sets {1,2,3,4,...}, {2,4,6,8,...}, and {...,-2,-1,0,1,2,...} all have cardinality Aleph_0, i.e they are all the same size as {0,1,2,3,...}. Its because of this that one might say something like infinity + 1 = infinity. The set of real numbers (R) can not be put into a one-to-one correspondance with the Naturals. R is somehow bigger. Its believed that R has cardinality Aleph_1, the first uncountable infinite cardinal number. (If i remember right, the continuum hypothesis states that card(R) = Aleph_1, but this is a hypothesis that can't be proven. It can be proven that there exists a first uncountable cardinal (Aleph_1), and the the cardinality of R is at least that big.) After Aleph_1 comes Aleph_2, then Aleph_3, and so on. It never stops. So my point is that its ok to assume that infinity is a number. And its ok to say that infinity + 1 = infinity, as long as you're aware of what you mean by it.
