I have a simple theory: Nothing is infinite unless the universe is infinite.
Let’s take an example of something we think is infinite. How about Real numbers? Say, between 5.0 and 6.0 there’s an infinite decimal place? How would we be sure? If we were to calculate it, it would only be limited to the amount the computer hold; thus, finite. What if we store the decimal numbers between 5.0-60.0 on a million computers? It still would be finite since there are limited amount of computers space. Another example: how about counting to a large number non-stop hoping to count to infinity? You’ll died soon. What about having someone take over that count? They’ll died soon! Eventually, someone might counting or maybe the earth might end in many billion years and thus the counting will be finite! Last example: the number of atoms in the universe if infinite, right? No! Unless the universe is expanding. There’ll be eventually a time when all the atoms are counted if the space in universe is limited, possible a gigantic number; however, the gigantic number wold be inferior to infinity.
So, my theory is nothing is infinite unless the universe is expanding! If not, the universe has a limit and thus, everything has a limit.
This assumes that you prove that a mathematical entitity is infinite by counting or calculation. In fact in mathematics you prove these things by techniques like proof by contradiction. You can’t prove something is infinite by counting because you would have to go on forever.
An example is Euclid’s proof that there are infinite primes. Assume the contrary. Then take the two highest primes, multiply them and add one. You have a new prime. Contradiction.
So we know that there are infinitely many primes without calculating all of them (which is obviously impossible).
You don’t get a new prime by multiplying two primes and adding one:
All primes are odd. Two odd numbers multiplied gives an odd number. Add 1 to an odd number and you get an even number. That even number cannot be a prime. (It is divisible by 2)
QED
Sorry. You are right. You have to multiply each of the finite (by assumption) primes and then add 1. You either get a new prime or a higher prime than the highest previously assumed. So contradiction.
One does not need to actually experience an idea or a phenomenon in order to know that it exists. As Cyberpundit is pointing out, the nifty thing about mathematics is that we can set up very, very finite algorithms that, when properly utilized, prove that there is, indeed, an infinite amount of numbers.
Heck, simplest algorithm there is to prove as such: x+1, where x is the highest known number. The product will be the next highest known number, and as such will go back around and be plugged into the equation again, where it will then be increased by 1…
In any case, such an algorithm can continue indefinitely.
You can’t count out an infinite number of primes in a computer. In fact, that what it means to be infinite.
It’s easy to find sets which are larger than any integer. For example, take the set of all positive integers, {1,2,3,…} For any integer N, this set obviously has more than N elements. That’s the definition of infinite. Being infinite doesn’t mean you can write all the elements down and count them out to infinity. It means you can’t write them all down and count them.
There are (theoretical; it’s not possible to draw them) geometric figures, like the Kock Snowflake that are infinite in length, but finite in enclosed area.
Infinity cannot be tangibly expressed in a finite domain, but it can certainly exist as a concept.
The assumption in that premise is that the universe is the only environment reality exists within. Inflationary Theory, a mainstay of cosmological models, insists there there are many universes all existing within an indeterminate medium.
The way mathematicians count numbers means that, for each integer, there’s another one after it that hasn’t been used before. And that is pretty much defined as infinite.
The universer isn’t infinite? Isn’t infinite in size? In detail? In time? Can you be more specific.
I understand what you guys are saying. Mathematically, it can be proven that there’s an infinite #. x+1. However, i was thinking in terms of something being infinite physically.
I understand what you guys are saying. Mathematically, it can be proven that there’s an infinite #. x+1. However, i was thinking in terms of something being infinite physically.
If the universe is physically finite, it’s necessarily mathematically finite as well. (Unless Infinite Computational Density is possible, in which case all bets are off.)
