Neighbors

For as long as anyone could remember, 4’s next-door neighbors on either side were 3 and 5.

Then one day, a new house stood between her house and 5’s.

4 marched up to the door and banged none-too-gently. “Who the hell are you?” she demanded.

The new neighbor smiled. They held a hand out as if to shake; 4 just stared blankly. “Nice to meet you! I’m $4\frac{1}{2}$.”

“Four-and-a-half? Who ever heard of four-and-a-half?” 4 muttered as she sipped tea with 3 later that day.

“You think that’s bad? Have you looked the other way?” 3 asked. “When I was coming over here I walked past another new house. The guy inside said his name’s $3\frac{1}{2}$.”

“What the fuck? Can they even do that? Just plop a house down and go ‘oh hey there I’m you-and-a-half’?”

“It doesn’t seem right,” 3 agreed.

The day after that, 4 found another new house halfway between hers and $4\frac{1}{2}$’s.

“And who are you?” she demanded sardonically. “4-and-one-fourth?”

“Um. Yes,” the new neighbor replied. “$4\frac{1}{4}$. It’s nice to meet you.”

“It’s not nice to meet you! You can’t just come waltzing in here—”

“4,” came 3’s voice, a bit shaken. “4, come here.”

4 huffed and walked away from $4\frac{1}{4}$’s front door. “What is it? Let me guess. $3\frac{1}{4}$?”

“That, and another one too. Says his name is $3\frac{3}{4}$. And that’s not all. About halfway between my place and $3\frac{1}{4}$’s is some douchebag named $\pi$.”

“What the hell is happening to our neighborhood?” 4 felt faint.

4 needed some fresh air. She packed a picnic basket and left, walking north a ways. There was nothing there, at least. Who could possibly move in up there, off the number line entirely?

But then she saw it. In the distance, a house. Outside, a woman was mowing the lawn.

“Howdy, neighbor!” the stranger called as soon as she noticed 4. “You must be $4+0i$!”

“I— excuse me?” 4 sputtered. “Who are you?”

“Me? I’m $4+i$. Been meaning to head down and say hello for a while now.” $4+i$ tilted her head in confusion. “Hey, wait, where are you going?”

4 turned around and walked away. If I never leave my house again, I won’t have to deal with this. Surely that was reasonable.