The Plane

may not have been, in which case we will receive however many. But we will get at least one new number, and it will be one different from the ones we started with, because none of those was a factor of our huge number.”

It was an odd train of thought, but Cold knew that she was still following. “Yeah.”

“And that's it. Given any amount of numbers of the set, we can construct at least one new one. And then another one. And another one. Or, probably much more than one, but one at least. If the set had finite size, we could take all of its members and construct at least one new one – so it can't have finite size.”

Cold thought about this for over five minutes, considering each step multiple times. Eventually, she was convinced that it was a definitive proof.

“Alright. Okay. Which shape for the infinite set?”

“The rectangle.”

Cold stepped at the edge of the shape. Breathing quickly, she hesitated for just a second, then she moved a front limb forward and touched the ground inside of it.

Both shapes disappeared immediately.

Nothing else seemed to have changed.

“What did it do?”

“I don't know. But I'm sure that we guessed right.”

Cold gulped. But there had never been a reason to assume that they would know that which they had gained. There were plenty of ways in which they could benefit without knowing about them.

“Alright. This has to be good enough.” Cold stood up. “Let's go. I want to bridge more distance.”

She began to move again, this time at a quickened pace. Then, less than two minutes into her walk, she could feel the next challenge incoming. Only... there was no threat. The challenge was coming, but not to them.

“Do you feel that?”

“Yeah. I think we get a free pass.”

“Oh.”

Cold verified this theory with her intuition. It was true. She could clearly feel the fifth challenge incoming, but nothing suggested that they had to do anything to be safe.

So this was the price they had won.

“Do you think this means that we just have to overcome a fixed number of challenges?”

“It doesn't have to. A free pass is valuable no matter what we have to accomplish.”

Indeed, a free pass would even then be valuable if all they could do was to delay the inevitable. This prize didn't provide them with any new information, but at least they were still alive. If they had ever had any chances, then they had also increased.

During the following minutes, Cold could feel the challenge taking place, even though it didn't take place for them. Breathing evenly, she continued to walk straight ahead, all the while on the lookout for anything that would contrast with the monotone blue ahead of her...

And then everything disappeared.