Texas Instruments TI-89 Tip List page 81

Warning: ∞^0 or undef^0 replaced by 1
I emailed TI Cares about this operation. Here is the response:
"An infinity symbol is necessary for doing limits, and if it is allowed as an argument or result of the limit
function, then something must be done when it is combined with other expressions.
"What the TI-92 does in such compositions is consistent with extended analysis. It is also consistent
with the ANSI standards for IEEE floating point arithmetic, and is the same as other CAS systems that
treat infinity. For example,
inf - inf => undef
1/inf => 0
abs(1/0) => abs(+-inf) => inf
and
inf - 100 => inf
"For transformations such as the latter, it might help to think of inf as representing a whole set of
numbers rather than a single one.
"In order to obtain sharp results in computer algebra, it is important to discard as little information as
possible throughout each computation. For example, this is absolutely crucial for internal computations
of limits, which is done recursively via rules such as the limit of an absolute value is the absolute value
of the limit of the argument.
"It is true that at the more elementary levels of math education we lump more into the phrase
"undefined", which therefore doesn't have a single definition. Rather, it means "I don't want to talk
about that yet."
"However, for consistency, the computer algebra must implement one place along this spectrum of
sophistication. Unless the place is "discard as little information as is practical", people will be
disappointed that the product can't do certain limits, definite integrals, solutions of equations, etc. that
are in standard math tables and relevant textbooks.
"Actually, we did weaken the product somewhat to appease the more elementary end of the spectrum:
+-inf is necessarily carried internally, but it is degraded to undef during output. This is why abs(1/0)
simplifies to inf but 1/0 is displayed as undef: Compositions can be more powerful than stepwise
computations such as 1/0 STO foo: abs(foo). This is additional evidence that the only easily explained
places on the spectrum are: a) No infinities: only undef as on typical purely numeric calculators; or b)
Make it as powerful as is practical. The first choice is simply not an alternative if there is a desire to do
symbolic limits, improper integrals, etc.
"I am sorry that a single product can't exactly match the needs of education from beginning algebra
through second-year calculus. We chose to make the product as powerful as we could within the
constraints on ROM and programming time. Many teachers have found that the excess power for
some classes stimulates the students curiosity and provides opportunities for lively discussion. It also
allows the students to buy a single calculator that suffices for a succession of courses."
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