I may have misread it, or it isn't mentioned at all. Looking at the Prentice Hall tutorial (this is a very advanced calculator) it says the following on the TI-82...

The order of operations is programmed into the calculator. It performs the operations just as in algebra. The expression, 1 + 2 x 3 is calculated as 1 + (2 x 3). Since parentheses always have the highest priority, use extra parentheses whenever in doubt. The expressions (9 + 16)^1/2 and 9^1/2 + 16^1/2 are not equal.

I have a lot of reading to do just to begin to use this sucker. One of the sites I found are cracks for it to play games and display pictures. Seems Cindy Crawford is popular with this site master, who freely admits he's a teen (or used to be).

http://kbbl.tripod.com/ti82.html

So, the test that tells is the equation itself.

And it says the answer is 2.

 

The expressions (9 + 16)1/2 and 9^1/2 + 16^1/2 are not equal.

No 5h17, Sherlock...

(hint: use a translator if your leetspeak is rusty)

 

I didn't know you were a script kiddy!

 

I 'm not, I could never see myself as a dedicated programmer. But on the other hand I love internet trends and leetspeak is one of them.

Speaking of internet trends, one of my favourite sites is www.knowyourmeme.com

P.S. I 'd love to hear what a TI (or similar company) employee would say on the matter too.

 

P.S. I 'd love to hear what a TI (or similar company) employee would say on the matter too.

I found an online manual chasing down this topic from TI on their scientific calculators. Sorry I did not keep the link and could not find it, but basically they started giving implied multiplication a higher priority, but later dropped this feature.

I wonder if some of this confusion is due to TI locking up the technique with a patent!

Electronic data processing apparatus with equation operating system having implied multiplication of two hierarchical ranks

Abstract

The equation operating system is an improved data and command entry format together with a compatible operation system for use with electronic data processing apparatuses, most particularly with scientific calculators which provide an alphanumeric display of entered equations. This invention provides an implied multiplication having differing hierarchical ranks when one of a member of a predetermined prefix set entry is followed by one of two differing suffix set entries. Each of these implied multiplications have a differing hierarchical rank than that of explicit multiplication.

Inventors: Caldwell; David (Lubbock, TX), Ferrio; Linda J. (Lubbock, TX), Hunter; Arthur C. (Lubbock, TX)
Assignee: Texas Instruments Incorporated (Dallas, TX)
Appl. No.: 06/381,985
Filed: May 25, 1982

 

The term MDAS as discussed in basic math can work as M/D A/S, which means that multiplication can be interchanged with division and the same goes for addition and subtraction. In this case, I would find the equation to yield 2. The () there does not really signify any operation so that describes that you should distribute it first inside and not take it as a regular multiplication operation. It may have been explicitly described as a common factor to 9 and 3, that's why it was taken out.

 

Very interesting! Thanks for that info. I think "degenerating" may be too derogatory a term. "Evolving" seems more accurate and less judgemental, as evolution often includes general simplifications and improvements where some less-used things are lost. You wouldn't say ships have "degenerated" to using GPS nav instead of a sextant, even though there may be a loss of some of the older skills.



That's pretty much exactly what a compiler would do to the math. Either autoinsert the missing * operator or signal an error because of the missing * operator. Windows 7 may use a javascript component for the math which will be almost identical to the C compiler math.



Interesting that you bought a calc that gives you the answer that you prefer and i bought one that gives me the answer I prefer... Nobody wants an argumentative servant!

May I ask what year the calculator is and what the exact wording is in the manual? I'm interested in trying to narrow down the year where the precedence went from being "mathematically correct precedence" to "traditional math precedence".

I'm sure TI whose reputation is based in a big part on their calculators have some real smart math PHDs that have not taken this issue lightly. Wouldn't it be great if we get one of them to post here?

What will all of this do if anything to all of the calculations and formulas that the world of science and physics depend on? If the sequence of math changes won't the results of "sacred" formulas change too?

 

Nah. Maybe some Excel spreadsheets will stop working but a seasoned engineer and/or scientist knows what the formulas mean, formalities are just the details.

 

...
I wonder if some of this confusion is due to TI locking up the technique with a patent!

Cool info! Lodged 1982. That would have been about the start of handheld calculators becoming "smart". I remember a couple of TI handheld programmables about 1982 that cost hundreds of dollars and had the old red 7-segment displays. Wedge-shaped things.

What will all of this do if anything to all of the calculations and formulas that the world of science and physics depend on? If the sequence of math changes won't the results of "sacred" formulas change too?

I don't think the results as such will change. But it's logical that as people integrate more with machines we will adopt the simplest standards for entering data into the machines. Like the way you would use a simplified English sentence to enter data into a google search, because it would give you the best output.

So it stands to reason that where precedence is important it would be more clearly specified in future texts, and specified in the simplest form as future texts would likely be produced and distributed in linear text format or have people copy formulas from the text into machines in linear text format.

So you might see something like; Xc = 1/(2 pi f C) or even; Xc = 1/(2*pi*f*C) within the text rather than as some special graphic image or special symbols or a possibly corrupt linearisation like; Xc = 1/2pi f C

 

The term MDAS as discussed in basic math can work as M/D A/S, which means that multiplication can be interchanged with division and the same goes for addition and subtraction. In this case, I would find the equation to yield 2. The () there does not really signify any operation so that describes that you should distribute it first inside and not take it as a regular multiplication operation. It may have been explicitly described as a common factor to 9 and 3, that's why it was taken out.

Actually, no, but then you haven't read this thread in its entirety, and missed the explanations this is so. The standards have changed over time, but I suspect the old school will survive with the math professionals given the proofs I've seen.

Of course, the real gist of this thread is parenthesis are our friends.