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==
{{incomplete|Created by a SECOND BOT TO REDUCE CONGESTION - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
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 at π. The new branch maintains the same scale-separations as the 'normal' one (as far as it goes) but, due to a longer initial curve away from the junction, the new-branch digits are also consistently slightly offset from the horizontal positions of the respective old-branch ones.

The sequence ending with a bold mark at Δ (whereas the original number line fades out) 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 been {{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" stops at every integer. Powers of 2 are 2, 4, 8, 16, 32, and so on, 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." 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 ''numerals'' were shown in [[2206: Mavis Beacon]]. And 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 bifurcation 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 with two short horizontals 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]]