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It's plenty correct mathematically; the linked article even explains this. Generally, your viewpoint comes from an incorrect understanding of mathematics, so l
by Zarel 8y ago
It's plenty correct mathematically; the linked article even explains this.
Generally, your viewpoint comes from an incorrect understanding of mathematics, so let's explore what math actually is:
When we say "10 / 2 = 5", the result "5" doesn't come out of nowhere. It comes out of the definition of division.
There are several ways you could define division. You could interpret "10 / 2 = 5" as meaning any of:
• "If you had a 10-inch stick and you divided it into 2 equal parts, each part would be 5 inches."
• "If you had the equation 2 * X = 10, X = 5 would be a solution to it."
• "If you had 10 Pa of pressure in an enclosed box, and you increased the volume of the box to 2 times its previous volume, its new pressure would be 5 Pa."
• "A wave of wavelength 2cm would have a frequency of 5 per 10cm."
These definitions all lead to the same result – in other words, they're equivalent. When this happens, mathematicians usually don't particularly care which one is the "real" definition.
This applies to many different mathematical axioms. For instance compare the definition of the Parallel Postulate on Wikipedia:
"If a line segment intersects two lines, the two lines will intersect on the side that their angles with the line segment sum up to less than 180°"
– https://en.wikipedia.org/wiki/Parallel_postulate https://en.wikipedia.org/wiki/Parallel_postulate
with the definition on Wolfram MathWorld:
"If you have a straight line and a point not on it, there exists only one straight line which passes through that point and never intersects the first line."
– http://mathworld.wolfram.com/ParallelPostulate.html http://mathworld.wolfram.com/ParallelPostulate.html
These are different definitions. But since they lead to the same result, mathematicians don't really care to argue over which is the "real" definition.
Some definitions only apply over a subset of numbers. For instance, originally, "5 - 10" was undefined. Then negative numbers were invented, to expand the definition. The same thing happened with square roots and complex numbers.
That's the same thing with division. 1 / 0 was originally undefined. But you can come up with new number systems that define it, while preserving all the other properties that make division what it is. A common definition is 1 / 0 = Infinity, which is done in the Riemann sphere number system:
https://en.wikipedia.org/wiki/Riemann_sphere https://en.wikipedia.org/wiki/Riemann_sphere
There's nothing mathematically incorrect about doing any of this.