How Can Irrational Number Never Repeat?

I was hoping someone here could help me with this one. Because I just can't wrap my mind around it.

Numbers like one-third, when turned into a decimal, don't terminate but also repeat. .333333333333333333333333333333333333333333333333333333333333333333...

I can wrap my mind around this. But what about irrational numbers? Like π? Or even square root of two, or three and so forth? There are so many. They don't terminate but never repeat. How can something never repeat and yet go on into infinity? To me that seems odd.

Please at the very least tell me something that makes it a little more clear, what we're dealing with here.

 

Well... They are irrational.

irrational

/i(r)ˈraSH(ə)nəl/

adjective

1. not logical or reasonable.

"irrational feelings of hostility"

 

Pi, or the Golden Ratio, has turned out to not be entirely random, but to express a multidimensional multifractal equation. It doesn't repeat, and the equation could go on forever, but that will have to wait for quantum computers. The only odd thing about mathematics, is that most of the current math we use is based on two thousand year old outdated metaphysics, and is grossly outdated and misleading. The Umbral Moonshine Conjecture has been established, making it theoretically possible to measure infinity in the real world, if you want to check it all out for yourself but, my own belief is, nobody ever said either mathematics or life had to make sense, in the final analysis.

 

On the "One Million Digits of Pi" page, the first 6 digits 141592 only repeats once. 14159 repeats 15 times. 1415 repeats 93 times. 141 repeats 995 times.

There are probably other sequences that repeat more frequently.