Floating point: insignificant differences add up to large differences.
Mathematicians defining limits: *sweat nervously* "So um (*Autistic screeching*) well, the limit is just the sum of series, basically(*inhales*): Its the result. The Science is Settled."
The modern definition of a limit (for any ε there exists an index N so that ...) was given by Bernhard Bolzano (Der binomische Lehrsatz, Prague 1816, little noticed at the time), and by Karl Weierstrass in the 1870s.
https://en.wikipedia.org/wiki/Limit_of_a_sequence#History
I find it ironic people can intuitively understand why material object speed can only approach c, but be never equal to it.
Imagine an object that is traveling at 0.9c accelerating to 0.99c(+0.09c)
1.each hour the object accelerates by 10% of previous acceleration.
e.g. 0.9c,0.99c,0.999c,0.9999c
2.Will its speed will be equal to c at any time?
>>14 Speaking of autistic screeching, this is how they justify the modern concept of a 'limit' equal to result.
https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit#Informal_statement
https://en.wikipedia.org/wiki/Archimedean_property
These two are just arbitrary axioms that are convenient for modern theory, without correctly representing reality(same thing with "quanta of energy" see https://archive.org/details/arxiv-1005.1058 ) but
People often comment that Math is divorced from reality, but they can't explain how. Its the continuum
https://en.wikipedia.org/wiki/Continuum_(measurement)
Reality isn't a VR sim with pixels(or 'quanta' in physics terms).
Math is modeled on theory which excludes infinitesimals, introducing the idea of 'minimal object' above zero(the Quanta of Math is the first real number above) of which all numbers have a finite quantity thereof(since its the smallest element to which numbers can be decomposed into, because infinitesimals can't exist in Modern Math) like pixels; this is of course the reductio ad absurdum of archimedean property.
This "Virtual Reality Math" only works until its foundations are investigated logically..but people follow what is convinient