1/x = 0
1 = x*0
You may think that x*0 is always 0 and therefore this equation has no solutions, this is usually the case but when x=infinity it's actually indeterminant, ie the limit of n* k/n as n goes to infinity is k, so infinity*0 can equal 1, no other number has this property so if there is a solution to 1/infinity it must be 0
By the same argument as 0.999... = 1, we have
1/10 = 0.1
1/10^2 = 0.01
1/10^3 = 0.001
1/10^infinity = 0.000...
10^infinity = infinity, and the decimal expansion of 1/infinity is the same as 0, because they are the same number.
Finally, we have
1/infinity * k = 1/(infinity/k)
infinity/k = infinity for all real k, meaning multiplying 1/infinity by any real number equals 1/infinity, this implies 1/infinity is 0 because adding 1/infinity to itself adds 0.
1 = x*0
You may think that x*0 is always 0 and therefore this equation has no solutions, this is usually the case but when x=infinity it's actually indeterminant, ie the limit of n* k/n as n goes to infinity is k, so infinity*0 can equal 1, no other number has this property so if there is a solution to 1/infinity it must be 0
By the same argument as 0.999... = 1, we have
1/10 = 0.1
1/10^2 = 0.01
1/10^3 = 0.001
1/10^infinity = 0.000...
10^infinity = infinity, and the decimal expansion of 1/infinity is the same as 0, because they are the same number.
Finally, we have
1/infinity * k = 1/(infinity/k)
infinity/k = infinity for all real k, meaning multiplying 1/infinity by any real number equals 1/infinity, this implies 1/infinity is 0 because adding 1/infinity to itself adds 0.
