# Divided by itself equals 1?

The Rev
Is it a reasonable statement to say either:

1) $$\frac{\infty}{\infty} = 1$$ ?

2) $$\frac{0}{0} = 1$$ ?

$$\phi$$

The Rev

Homework Helper
No. Those are not well defined operations, and infinity is not a number. In classical analysis this problem is dealt with by considering limits.
Such as
$$\lim_{x\rightarrow a}\frac{f(x)}{g(x)}$$
in the case when if f and g both go to 0 (or infinity) as x goes to a
further analysis is needed to decide the limit
These are called indeterminate forms since the rule about a limit of a combination of functions being equal to the individual limits combined the same way does not apply.
There are several forms of indeterminate forms that commonly occur
0/0
infinity/infinity
0^0
1^infinity
infinity-infinity
0*infinity
1/0-1/0

The Rev
Is this how they cancel out infinities in renormalization in QM?

Homework Helper
Is what how they canceled out infinities in renormalization? WIth infinite stuff physicists can and do simply ignore things (nothing to do with cancelling), and annoyingly it all seems to work. Hre is a link explaining it in non-specific language:

http://math.ucr.edu/home/baez/renormalization.html

The Rev
Well, he lost me at Lagrangian, but I did get the feeling that renormalization isn't about cancelling out infinities with simple division. (I know nothing of this higher level math, yet.)

I was impressed, however, that singer Joan Baez is also an expert on Quantum Mechanics.

$$\psi$$