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.