If a rational number is a number that can be represented in a fraction that comprises of 2 rational numbers, then shouldn't numbers like 1/0, 2/0, etc, be rational numbers as well?
So if you take that and go backwards, and divide by 0, what is your answer? Is it 1, 2, or 3?
Since there are infinite numbers that, when multiplied by 0 give you 0, it is undefined what the answer is when you go in the reverse direction. If you allow dividing by 0, you can get nonsensical answers like 1 = 2, which is obviously incorrect.
Side note to start: I'm having a weird issue where my instance can't see comments on this post, and I checked and there is no defederation or blocking. Not sure why.
I would, first of all, probably correct the definition of a rational number: A rational number is a number that can be represented as a ratio (fraction, quotient) of two integers, not other rational numbers. This should keep the definitions easier to use, and not self-dependent.
As for the actual meat of the question, I would argue that division by zero results in something that is not a number at all, and it must be a number to be a rational number. Others will (and have) simply define(d) rational numbers to not include division by zero, or to define rational numbers as an integer over a natural number (naturals being 1, 2, 3...).
How you define things in mathematics changes how you use it heavily. If you had a field or branch of mathematics that had a working definition for division by zero, numbers like 1/0 and 2/0 would likely be rational in that context.
3 Comments
Afrazzle@sh.itjust.works · 8 pts · 3y
A rational is a number that can be represented as a quotient with integer numerator and non-zero integer denominator. So x/0 is not rational.
MrPoopbutt@lemmy.world · 4 pts · 3y
0 * 1 = 0 0 * 2 = 0 0 * 3 = 0
Therefore 0 * 1 = 0 * 2
So if you take that and go backwards, and divide by 0, what is your answer? Is it 1, 2, or 3?
Since there are infinite numbers that, when multiplied by 0 give you 0, it is undefined what the answer is when you go in the reverse direction. If you allow dividing by 0, you can get nonsensical answers like 1 = 2, which is obviously incorrect.
EnderofGames@lemmy.ca · 2 pts · 2y
Side note to start: I'm having a weird issue where my instance can't see comments on this post, and I checked and there is no defederation or blocking. Not sure why.
I would, first of all, probably correct the definition of a rational number: A rational number is a number that can be represented as a ratio (fraction, quotient) of two integers, not other rational numbers. This should keep the definitions easier to use, and not self-dependent.
As for the actual meat of the question, I would argue that division by zero results in something that is not a number at all, and it must be a number to be a rational number. Others will (and have) simply define(d) rational numbers to not include division by zero, or to define rational numbers as an integer over a natural number (naturals being 1, 2, 3...).
How you define things in mathematics changes how you use it heavily. If you had a field or branch of mathematics that had a working definition for division by zero, numbers like 1/0 and 2/0 would likely be rational in that context.