If 1/0 is infinity and 2/0 is infinity, why isn't 1=2?

Sep 30, 2020
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Short answer: 1 times 0 is 0, 2 times 0 is 0 but 1 isn’t 2. It’s the same thing.
For a long answer, take this example:
You have a list of all positive integers. How long would this list be? You’d always go on to the next integer; if you are at 2000 integers, you can increase the amount of integers to 2001, and so on. This list would of course be infinitely long.
Now we’re going to take a list of all positive EVEN integers. Would this list be smaller, longer or just as long as the previous list?
The answer is: it’d be just as long. For example, if you had the numbers from 1 all the way up to 1000 in the first list, you can always use all the EVEN numbers from 2 to 2000 to have a list of the same length. This means that 2 times infinity is the same as one infinity.
Now back to your question. If 1/0 equals infinity, then 2/0 would be the same as 2 times 1/0, which would be the same as 2 times infinity, but 2 times is one, so that’s why 1/0 is infinity, 2/0 is infinity but 1 is not 2.
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Nov 18, 2020
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Since infinity is unmeasurable, then in comparison 1 & 2 are in a sense unnoticed or rounded to an equal state, therefor equating an equal value which would then generally be normalized as 0. - conceptual mathematics.
Nov 19, 2020
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Infinity is not a number. It is a concept, as stated much better above me lol.

When you resolve the fractions, you don't get 1 and 2. You get 0 and 0, hence, infinity.

A better way of writing out '2/0' is 'two zeroeths'. What is a ratio of two to zero? there isn't one. this doesnt not equate to a number, it's a concept. the answer doesn't matter.
even easier to express it like this.
To get rid of the 0s, you have to multiply both sides by the lowest common denominator. That happens to be infinity, or zero. Same thing.

1/0(∞) = 2/0(∞)
1(∞) = 2(∞)
since 2 infinite is equivalent to 1 infinity, (as they are meaningless, you can just express it as
∞ = ∞

1/0(0) = 2/0(0)
0 = 0

more strictly, 2/0 = #DIV/0!
Nov 28, 2020
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But, 2/0=1/0= infinity, out of context, means that both ratios are large without limit, not that 2=1.

When you divide 10 by 2, you get 5, because there are 5 "2's" in 10. When you divide 10 by 0, you get no single numerical result of any use to most of us.

However, if you define 0 as a limit of a series of numbers that get smaller and smaller, then
2/(number in the series) gets bigger and bigger. In mathematical modeling of the physical world, this could mean an instability leading to disaster, or a singularity that is not intuitively related to a physical process.

If the number in the series is the same for both 1/number and 2/number, then, as the numbers in the series get smaller, 2/number will be twice 1/number at each number in the series. E.g.,

Series 1, .5, .25, .125, .0625, ...., approaching as small a number as close to zero as you like

2/number is itself a series: 2, 4, 8, 16, 32 ...., always twice the value at each step
1/number is itself a series: 1, 2, 4, 8, 16 ...,

so, (2/number) = 2 times (1/number), for all values of the number as it gets smaller and smaller.

The use of the word infinity means that there is no end to the increase in size of these ratios.

Disclaimer: Mathematicians will always humble me in this sort of discussion.
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I understand division by zero to be undefined; i.e.: call it infinity, call Charlie. Basically, any multiplication by zero is the equivalent of doing nothing i.e.: the product is zero, a place holder on an arithmetic scale.