Editing 2956: Number Line Branch

{{comic
| number    = 2956
| date      = July 8, 2024
| title     = Number Line Branch
| image     = number_line_branch_2x.png
| imagesize = 469x235px
| noexpand  = true
| titletext = Attention all passengers: This is an express sequence to infinity. If your stop is not a power of two, please disembark now.
}}

==Explanation==
This comic likens the {{w|number line}} to a line of a railroad or subway system. These often have branches where different trains continue on to a different destination, with different stops along the way, or travel on parallel lines to allow faster trains to bypass slower ones. In the number line, one branch (presumably the original) contains ordinary numbers, while the newly opened branch consists of some completely different numbers, denoted with various symbols as an analogue to those we use as digits. The branches seem to split around π. The new branch maintains the same distance between numbers as the 'normal' one (as far as it goes) but, due to a longer initial curve away from the junction, the digits of the new branch are also consistently offset slightly to the left from the horizontal positions of the respective digits of the normal branch.

The new branch ending with a bold mark at Δ (whereas the original number line fades out after 10) suggests that it is the end of this branching sequence. Mathematicians, apparently, could only afford to construct 5 additional numbers, or their research hasn't yet found other numbers. The branch may have been intended to run much further, but it was possibly {{w|High Speed 2#Cancellation of Phase 2, October 2023|scaled back}} due to budget overruns and cutbacks.

The title text makes a parallel between a train stopping at a station and a numerical sequence "stopping" at a number – that is, taking it as a value. It's a spoof of announcements that are typically made on trains, so that passengers can confirm that they're on a train that goes to their desired station; an "express train" typically makes fewer stops so it can serve the most popular stops and reach its final destination sooner. In this case, the express train only stops at powers of 2; presumably the "local" train stops at every integer. Powers of 2 are 2, 4, 8, 16, 32, ..., 2<sup>n</sup>, such that the interval between stops grows exponentially larger.

Mathematically, an express train like this would get to its scheduled stops much faster, but it would not actually have any fewer stops overall. Mathematicians that study infinities generally regard all "{{w|Countable_set|countably}}" infinite sets as being the same size (containing the same number of elements). Infinity is not a fixed value; rather, it's the concept of "does not end", so it's paradoxical to try to take a train to a destination that is, by definition, not a single destination. By way of analogue, it's akin to promising to stop hitting your little brother only after you've done so forever.

A fictional number was previously shown in [[899: Number Line]] ("gird"), and fictional <em>numerals</em> were shown in [[2206: Mavis Beacon]]. Similar treatment of mathematics as public infrastructure was seen in [[2735: Coordinate Plane Closure]].

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[A diagram reminiscent of both the number line and a transit system diagram. The line starts at the left and goes right through points labeled 0, 1, 2, and 3, at which point there is a split into two branches. The top branch continues: 4, 5, 6, 7, 8, 9, 10, …. The bottom branch is shorter, labeled with five curious glyphs: a square, a near-vertical line with two short horizontal lines jutting out from it, a phi-like/lollipop symbol, a spiral, and a delta/triangle symbol.]

:[Caption below the panel:]
:Good news!
:After thousands of years, mathematicians have finally opened a second branch on the number line to reduce congestion.

{{comic discussion}}

[[Category:Math]]