TI84 plus really that clumsy??



#13

This my son's forth day in his 7th grade algebra class. His teacher passed out the classroom set of TI84 plus's today, and they ran through some real simple single argument keyboard functions on them. According to him (my son) a function like
x^2 is keyed in: function key first, then the argument, then enter (it seems like the old TI's used RPN sequence for single argument functions, or is my mind playing tricks on me??). Anyway, I then asked him how one used the result of a previous calculation as the argument for a single aurgument function on this wonderous machine, and he said the argument had to be memorized and keyed in again after the function key was pressed. Surly this can't be right!! Can someone familiar with modern TI stuff please tell me how to use an existing value as an argument without having to key it in again, so I can relay it to my son to save him some time (he's not allowed to bring the classroom calcs home, or (I think) I could figure it out myself).
Thanks, and best regards, Hal


#14

Chain calculations are easy:

1+2 ENTER
+3 ENTER
*5 ENTER

The display shows how this is done: The reserverd variable "Ans" is pasted into the command line if you start with an infix operator. To use "Ans" somewhere inside a calculation, press 2ND and then (-). The Ans function is labled above the key.

The sequence 2ND ENTER, labled ENTRY above the key, scrolls through the last few expressions and commands entered.

Marcus

Edited: 1 Sept 2006, 4:21 a.m.

#15

Hi Hal. Also, tell your son to be careful with the TI-8x series as it interprets -2^2 as -(2^2) instead of (-2)^2.

Regards,

John


#16

Hi, John:

John posted:

" Also, tell your son to be careful with the TI-8x series as it interprets -2^2 as -(2^2) [...]

    As it should. That's the correct way of interpreting -2^2, and the HP-71B does exactly the same, returning -4. If you want (-2)^2, you should write it that way, parentheses and all.

    If in doubt, check any math books or articles and look for terms such as -a2 , you'll easily find them aplenty. Do you really think the author actually intends you, the reader, to interpret that term as (-a)2 instead ? Unary minus has lower precedence than exponentiation in standard math writing.

Best regard from V.

Edited: 4 Sept 2006, 3:23 p.m.


#17

Hi Valentin. You are correct, however different machines interpret this differently. A sample of today's $15 EOS calculators reveals the following:

- TI 34II, Casio FX-115 and HP 30S yield -4.

- Sharp 506 inserts parentheses and yields 4.

The HP 33s in algebraic mode also inserts parentheses and yields 4.

All I'm saying is that one needs to be familiar with the nuances of each particular system that one uses.

Regards,

John

#18

Quote:
Unary minus has lower precedence than exponentiation in standard math writing.

I agree -- I always assumed that -x is basically just a shorthand for 0-x, and that's how unary minus (and plus) behave in mathematics texts.

In CompSci textbooks, however, unary minus is universally treated as a completely different beast than binary minus, and given much higher precedence. I've seen this in numerous parser examples, and actual languages like C and its kin (C++, Java, JavaScript, etc.) are also like this... Although those languages lack a power operator, which saves them from embarrassing themselves by mis-interpreting expressions like -x2.

- Thomas


#19

Interesting thread...

I pulled out my 49g+ and played around with -x^2 and I got different results depending what function I used. By entering -2 and using the x^2 function, I got 4. By using -2 y^x 2 enter, I get -4.

Why the different answers?

Gerry


#20

Quote:
I pulled out my 49g+ and played around with -x^2 and I got different results depending what function I used. By entering -2 and using the x^2 function, I got 4. By using -2 y^x 2 enter, I get -4.

Why the different answers?


Because you're calculating two different things :-)

The x^2 function squares the object at the top of the stack, so -2 x^2 calculates (-2)^2 -> 4.

-2 y^x 2 calculates -2^2 which, as mentioned earlier in the thread, evaluates as -(2^2) -> -4.


#21

Kiyoshi:

I understand your point so it seems I didn't make my question clear enough. I used equation writer to evaluate both expressions and got the expected results as you described using both the x^2 and y^x commands and parentheses. I also understand that by putting 2 in the first level of the stack (in RPN mode) and executing X^2, the result will always be positive.

What is confusing me is that when I use the x^2 command, there are no parentheses in the display to clarify what will happen first. For instance, in ALG mode, push x^2 and you get "SQ()", enter -2 and you get 4. If I write that down on a piece of paper, it would be -2^2 which is -4, not 4. Perhaps the 49g+ is getting around this by using the syntax "SQ()" which would be evaluated as the square of the argument and that will always be positive. If you do -2 y^x 2, the display is -2^2 and you get -4. This means that there are situations where the functions x^2 and y^x give different answers.

I think my confusion boils down to this. I always considered the calculator function x^2 and specialized version of the calculator function y^x. What's being said here is that this is not true and here is an example where the two functions evaluate to different answers. That twists my brain but am I correct?

Gerry


#22

Quote:
What is confusing me is that when I use the x^2 command, there are no parentheses in the display to clarify what will happen first. For instance, in ALG mode, push x^2 and you get "SQ()", enter -2 and you get 4. If I write that down on a piece of paper, it would be -2^2 which is -4, not 4.

I beg to differ. If I put the -2 inside the parenthesis as "SQ(-2)", I would write that down as (-2)^2, which is 4.
Quote:
Perhaps the 49g+ is getting around this by using the syntax "SQ()" which would be evaluated as the square of the argument and that will always be positive. If you do -2 y^x 2, the display is -2^2 and you get -4. This means that there are situations where the functions x^2 and y^x give different answers.

Precedence of operators. ^ has higher precedence than -, just as * has higher precedence than +.

In this case, x^2 and y^x are giving different answers because they are given different arguments (actually, the answers are the same, one of them has an additional operator applied after). -2 y^x 2 displays as -2^2 and is interpreted as -(2^2). You don't see the parens but they are there. If you enter (-2) y^x 2, it displays as (-2)^2 and gives 4.

Quote:
I think my confusion boils down to this. I always considered the calculator function x^2 and specialized version of the calculator function y^x. What's being said here is that this is not true and here is an example where the two functions evaluate to different answers. That twists my brain but am I correct?

x^2 is indeed a specialized version of y^x. It's the location of the - that's making the difference. Is it negating the 2 before the squaring or is it negating the result of the squaring? In one case you're negating 2 to get -2, then squaring -2 and getting 4. In the other case you're squaring 2 to get 4, then negating the 4 and getting -4.

Try evaluating '-3!'. Is that the factorial of -3 or the negative of the factorial of 3? In other symbols, is it -(3!) or (-3)! ? The same principles apply.

Hope that didn't muddy the waters even more.


#23

I may be mistaken here, but why is it squaring and then negating with one operation and negating and then squaring with the other. If I place -2 in the stack, shouldn't the calculator take -2 to be the object. I do not know of any operation that separates the object into two different objects. Unless creating lists or similar types. But in RPN if I have

4:
3:
2:
1: -2

and then calculate SQ I should expect 4

on the same token if I have

4:
3:
2: -2
1: 2

and then press y^x I should also expect 4. There should not be a reason to split the object into 2 and NEG. So in algebraic form why do the following provide different meanings:

-2 x^2 = 4
-2 y^x = -4

I agree with Gerry, they should give the same answer.

Osvaldo Rodriguez

Edited: 6 Sept 2006, 11:14 p.m.


#24

Hi Osvaldo. To further the confusion, in algebraic mode the HP 33s gives the answer of 4 for -2^2 and -2 y^x 2 after it inserts the -2 in parentheses in both cases.

This reminds of why the unambiguous nature of RPN appealed to me when I was first exposed to it.

Regards,

John

#25

The difference is that in equation mode the 49+ (or my 48G) breaks down the equation -2^2 into all its component parts and then applies the rules of mathmatical heirarchy to them. The exponent gets evaluated first, then the negative coeffecient. Resulting in -4. You have to put the -2 in brackets if you want it treated as one entity, and evaluated first. That the sign and the argument are evaluated first is implicit with the x^2 function key, but not in the equation writing / evaluating / algebraic realm. To echo the previous poster, this is why we all love RPN machines (in RPN mode!)...no paragraphs and no ambiguity

Regards, Hal


#26

To All:

Thank you all for your input to this discussion. It's obvious by now that this thread has migrated from understanding the mathematical difference between -2 x^2 and -2 y^x 2 as being (-2)^2 and -2^2 to how HP calculators evaluate these expressions. Kiyoshi, thank you for your explanation about presedence of the sign and power functions. It helped me a lot.

Osvaldo, you made a good point and I went back to your example and tried it in RPN mode for both my 48gx and 49g+. I put -2 on level 2 and 2 on level 1 and executed y^x. They both reported 4 as the answer. But, on the 49g+ in ALG mode, -2 y^x 2 returns -4.

Based upon this, it appears that similar keystrokes in RPN and ALG modes give different answers. Is this the unintended result of how the algorithms of these two modes interpret keystrokes or are there different assumptions being made in each mode?

Now that I've given this some thought, John your comments about the unambiguous nature of RPN takes on new meaning. Thanks.

I am really enjoying this!

Gerry


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