Indeterminates like 0/0 can be any number, depending on the limits of the function that leads to 0/0. For example, (sin(x)) / x leads to 0/0 when x=0, but its value is 1. Other functions have other values when 0/0 appears. So it makes no sense to invent a new number.
You can invent these symbols, but the actual values of interest are the limits as some variable takes an expression towards one of these indeterminate forms. For that you need L'Hopital's Rule, and other methods; and inventing a symbol for 0/0 will not have helped. Just one more piece of trivia to ingest.
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Indeterminates like 0/0 can be any number, depending on the limits of the function that leads to 0/0. For example, (sin(x)) / x leads to 0/0 when x=0, but its value is 1. Other functions have other values when 0/0 appears. So it makes no sense to invent a new number.
No, because they would be meaningless.
You can invent these symbols, but the actual values of interest are the limits as some variable takes an expression towards one of these indeterminate forms. For that you need L'Hopital's Rule, and other methods; and inventing a symbol for 0/0 will not have helped. Just one more piece of trivia to ingest.
0/0 = ©
0 = 0*©
Multiply both sides by ©
0*© = 0*©^2
Divide by zero
©^2 = ©^3
Divide by ©^2
1 = ©
So 0/0 = 1
Why didn't you say so in this first place?
lim x/x^2 = ∞
x-> 0+
lim x/x = 1
x-> 0+
So does ⊗ = ∞ or 1?