Infinity has to exist because it can be proven that there are an infinite amount of prime numbers. Euclid proved this a long time ago. If infinity didn't exist, then there couldn't be infinite prime numbers, right?
This is a pretty cool thread. It can probably be proved mathmatically. Even if the universe has finite boundries, what is to say that there are dimensions we do not percieve which are infinite, such as time or other universes.
It can be proved by thinking. Something cant come from nothing. Something exists. Something has always existed. Infinite existence = Infinity.
Ah, but numbers are just a model, an abstraction. They have no real value by themselves. Only when they represent something tangible can you say they represent real world phenomena. I've never said models can't be infinite. They can and do. Just divide 1 by 3, and hey presto, you got an infinite fraction of one. In reality though, divide a kilo of weed (I wish ) by 3, and you'll get a very finite result. Models are just that. Reality is a different beast alltogether.
I like your point, but say you divide the kil in 3 and you say you have a finite result. What that "finite" result depends on is the precision of the measuring instrument. If you weigh it with a more precise scale you'll see those 3's continue. Get an even more precise scale and they keep going. You can't get a scale precise enough to end in an 0. So to human perception, you have 3 equal shares, but measure it, and keep measuring it, you'll never end in truly equal shares. They just look equal. What this gets to is the debate of whether we can trust our senses. That debate goes back to ancient Greece (and possibly farther than that).
Infinity exist in increments, in which something happens then happens again and again etc... Just like yesterdays tommorow is the today of tommorow's yesterday. Thats an infinite statement. Pi is an infinite number, but it has incremental stages of that number. 3.14159 etc..... is the number but the .1 of the number is an increment. Just like the 4 and 1 behind that. Its Incremental Infinity. Depending on your religion, time in the state of reality is not infinite. But time in the state of subconscious mind is infinite. Nothing a man can produce can give an outcome of infinite proportions. Such as a toy on the market. For there to be an infinite amount of that toy. The production of that toy must also be infinite. And for that production of that toy to be infinite, so must the materials needed for that toy. And there are no infinite materials for that toy, except space. But even that is debatable.