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The alligator eats the big number

The alligator eats the big number

The alligator eats the big number

(OP)
I keep lurking on an editor's Facebook page, and somebody posted this. How to keep track of what greater than and less than mean.

A > B, C < D

Some engineering type replied with righty tighty, lefty loosey.

--
JHG

RE: The alligator eats the big number

...never needed anything to keep from getting comfused.bugeyed

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

When I was in grade school, much to the irritation of my father (RIP) who was on track to become a math teacher, it took me what seemed like the longest time to cope with those two symbols. Looking back I remain unsure why this was a problem, but I think that, to me, there was only one symbol and it just pointed to the small number. Giving it two different names when it only did one thing was, I'm fairly certain, the cause of the problem.

Just to soap-box on the failure in math teaching, and what isn't taught and should be -

Mathematics is discovered and has to be discovered independently by everyone who wants to use it, though that discovery process can be helped with a lot of hinting. What is taught in math class isn't mathematics. It is tools that are invented to describe the mathematical discoveries. And symbols like "<" and ">" typify that sort of invention. So what a math teacher is often doing is teaching the invention, which is often unclear to students who haven't discovered what the invention is for.

Parents (usually) teach children to count - the sounds and shapes related to that are arbitrary inventions as demonstrated by the wide variety in various cultures and languages. However it is up to the child (and eventually adult) to eventually discover the underlying math that the invention is used to externalize. I think the breakthrough must be the realization that one scoop of ice cream isn't as good as two.

Order of evaluation rules - an invention, arbitrary though convenient. Matrix representations - wonderful invention, and so on.

The sad part is that it is difficult to evaluate students on anything except mastery of the invention. Even so called Common Core/New Math, intended to fix this problem, is just another pile of arbitrary inventions which many students can use without discovering what they are for.

What I can say is that discovery doesn't happen just because a teacher is more insistent or gives a poor grade. It doesn't happen because the student is even more desperate. In this many math courses resemble the Saw movies where those trapped in the machine have to already know the way it all works to avoid injury. Small wonder that, in one book on teaching math, the author wrote that when he tried to figure out what goes wrong by asking adults about math classes the general response was a look of horror and a great desire to change the subject.

RE: The alligator eats the big number

I was helping the daughter of my wife's homecare giver with her Grade 12 math, and had a *.pdf copy of her textbook... it's far better than the texts we had, including university ones of 50 years or more...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

3DDave...

The Order of Operations isn't arbitrary...mostly. The OoO comes from the logic of mathematics, and is organized based on how we write equations and how most languages read. Kids are first taught (around 3rd grade, IIRC) that multiplication and division precede addition and subtraction, then later they are introduced to parenthesis and exponents and where they fit into the OoO. In the USA, they learn the acronyms MDAS, then PEMDAS. Unary operations such as factorial are left out because most students will never use them. They fit in between parenthesis and exponents.

Here is how the combination of logic and language leads to the OoO:
The most basic two-number operation in mathematics is addition. Subtraction is simply the opposite of addition (and is often thought of as adding a negative number), so it makes sense that neither addition nor subtraction have priority over the other. These two operations are thus performed left to right, in order, because most languages read left to right.

Multiplication represents repeated addition, and multiplications can be expanded into a series of additions, so it makes sense to evaluate multiplications before additions and subtractions. Division is simply the inverse of multiplication (and can be thought of as multiplying by the reciprocal), so it makes sense that neither multiplication nor division have priority over the other. These two operations are also performed left to right, in order, before additions and subtractions.

Exponents represent repeated multiplication, and exponents can be expanded into a series of multiplications, so it makes sense to evaluate exponents before multiplications and divisions.

Parentheses are used to modify the normal order of operations and get attention first.

There are some disagreements among mathematicians about how to handle certain things (e.g. is 6/2y equivalent to [6/2]*y or 6/[2y]?), but for the most part the OoO that people need for their everyday lives (and they do need it) is pretty simple and not subject to disagreement.

So, how do people use the OoO in real life? For starters, adding up the total value of a bunch of coins of different denominations or finding the total square footage of several rooms for calculating the amount of flooring to buy. The only way to get the correct answer, of course, is to multiply before adding.

Fred

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

RE: The alligator eats the big number

(6/2) * y by order of operations this is the correct meaning... It may be that the variable 2y is a distinct value, then it should have been written 6/(2*y). It depends on the intent.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

When I wrote "convenient," that's what it is. It doesn't represent the only way of expressing those operations. It's possible to simply evaluate from right to left. Or re-ordered left to right per RPN which has no parentheses required. Order of operations is arbitrary as long as all participants agree on how it is to be performed.

The area operation is exceptional as the units matter. Adding feet to square feet makes little sense. but for non-dimensional calculations: 5+4*4 could be interpreted as 5 enter, 4, plus, 4, times in a RPN variation to result in 36 rather than 21.

Or there could be a system that has no subtraction and depends on adding the 2s complement.

Thinking more on it - consider this progression

2 TIMES 2 IS 4.
2 X 2 = 4
2*2 = 4
2x = y

As the math gets more complicated the invention of symbols and meanings varies according to a mutually agreed upon basis. So 2x is somehow different from 23; the multiplication symbol has evaporated, having shrunk in each stage. I skipped the one where it's s dot; that dot is sometimes simple multiplication or represents the vector dot product, which makes no sense applied to a scalar value.

People are familiar with some invention so they think that it's the same as the math it is intended to represent or that it's the only way to do so.

RE: The alligator eats the big number

Funny how they have maintained their popularity... they originally started out as being fast... due to the 'stack' architecture of the processor. 50 years back I used to programme in forth... one of the few languages that could work in 'real time'... very similar to HP RPN... my current TI Nspire CXII CAS is almost as good, but I like the screen better. idea

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

Has this crap now entered ET like it has on Facebook? I hope not. Anyway, 3DDave, 5+4*4 = 21, not 36.dazed

www.PeirceEngineering.com

RE: The alligator eats the big number

It's actually 15. Welcome to hexadecimal.

RE: The alligator eats the big number

IRS... my wife used manipulatives for homeschooling our son... and they worked like a charm... depends on the type of learner...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

Quote:

depends on the type of learner

For sure. We never stayed the course, so I don't know what would have happened. Certainly, one concern I had was the hard association with physical things might make it more difficult to deal with the abstractness of the later math, like algebra, etc.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

RE: The alligator eats the big number

3DDave...

I will repeat, the OoO is not arbitrary, but comes from the logic of mathematics. Math is not ever done strictly left-to-right. Also, I have been using RPN since 1974 and I apply the OoO every time I work out a problem.

Fred

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

RE: The alligator eats the big number

Yes, it seems that recently there's been a lot of these, "what's the value of this formula" type questions on places like Facebook and such. My wife brings them to me and in each case, if one does not understand the 'Order of Operations', they get the wrong answer. And each time, I have to explain those rules to my wife.

John R. Baker, P.E. (ret)
EX-'Product Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: The alligator eats the big number

OoO isn't just a matter of convenience; we essentially have OoO when it comes to street stop sign conventions, i.e., straight trumps left turns and right-most trumps left. Without conventions we get chaos, as evidenced by Facebook, etc.

The examples chosen here are simplistic, but OoO follows the rules applied from evaluation of polynomials:

A*x^3 + B*x^2 + C*x + D

Think of the algebraic chaos if everyone did OoO differently, i.e., if exponentiation was trumped by multiplication, and addition trumped multiplication or exponentiation. No parentheses are required for the polynomial above, because OoO is automatically understood and applied. Therefore, no parentheses should be needed if the variables are replaced with actual numbers.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

RE: The alligator eats the big number

Note that back when I was writing programs on a regular basis, even though the languages and case tools that we were using understood OoO, I always used parentheses, if for no other reason than to make debugging easier for myself as well as anyone else who might have to dig through the source code. Granted, in the early days, particularly when we were still using punched cards, this was frowned on, but ever since editors abandoned the 80-characters/line limit, I felt that it was more of a personal preference than anything else.

John R. Baker, P.E. (ret)
EX-'Product Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: The alligator eats the big number

Sometimes math is done vertically.

All these arguments do demonstrate that the invention can completely overwhelm the underlying discovery.

"Math is not ever done strictly left-to-right." says someone who has never programmed in Postscript.

RE: The alligator eats the big number

(OP)
3DDave,

You need to try APL. There is no math hierarchy whatsoever, beyond brackets.

--
JHG

RE: The alligator eats the big number

Why would I use a language on the antiques list? Besides, I don't have an APL keyboard.

Haskell is the way to go, just ask the Haskell programmers.

By the by - my father was a systems programmer for IBM from the late 1950s. Plenty of wayside languages in his library. JOVIAL*, VULCAN, PL/1. But APL really stood out by needing a custom terminal to program in it (no GUIs to have virtual keyboards.) Though IBM did have some cryptic keys on their terminals anyway.

*not JUPITER - too many languages. crossed wires with recent Jupyter thread of Python.

RE: The alligator eats the big number

Quote:

There are some disagreements among mathematicians about how to handle certain things (e.g. is 6/2y equivalent to [6/2]*y or 6/[2y]?)

Interesting. I’ve never seen a term split arbitrarily like that, the use or lack of an operator is important as my 7th grade algebra teacher used to say. 6/2y = 6/(2*y).

RE: The alligator eats the big number

6/(2*y) is exactly how I'd read it too; no need for the parens putting it into a calculator. But I don't trust excel all that much so if I was entering it into excel I'd definitely be forcing the OoO by use of parens.

I’ll see your silver lining and raise you two black clouds. - Protection Operations

RE: The alligator eats the big number

6
2
y
mul
div

RE: The alligator eats the big number

In excel "=6/2*3" produces a result of 9. Thus the 2y is not held together and instead the division precedes the multiplication. In strictest terms, that is correct. But in more general terms, 2y is a thing that gets divided into 6 because 2y is implied to be (2*y). Using 3DDave's approach, you'd get what I expect, but not what you're likely to get from computational software. Typical software sees 6/2y as 6/2*y, wherein the division happens first and a y of 3 produces a result of 9.

If you're hand solving your own equation, go for it. Otherwise use parens to disambiguate it. Even if there's no ambiguity about it in the first place.

I’ll see your silver lining and raise you two black clouds. - Protection Operations

RE: The alligator eats the big number

If the OoO is known and correctly understood, parentheses should not be implied.

www.PeirceEngineering.com

RE: The alligator eats the big number

agree... to avoid any confusion and to make sure the correct intent of the equation is what you are really looking at.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

Quote:

I keep lurking on an editor's Facebook page, and somebody posted this. How to keep track of what greater than and less than mean.

A > B, C < D

Some engineering type replied with righty tighty, lefty loosey.
I never had trouble with that one that I can recall. It seems strange that someone would be asking how to remember it...

BUT the image that comes to mind immediately is that the vertical distance between the two lines corresponds to the relative size of the operands. The side of the operator where the vertical distance is big corresponds to the big operand and the other side where the vertical distance is little/zero corresponds to the little operand.

I wonder if that's something that was taught to me way back in grammar school and faded into my subconscious. I'm guessing it probably was.

At any rate that seems way more intuitive than righty-tighty / lefty loosie. I'm not even sure how RT/LL helps us remember anything (outside of valves, fasteners, and most importantly... beer bottle caps!). Maybe you're supposed to focus on the L's in lefty-loosie and think "Less than"? Or maybe it was just a wise-crack making fun of the person who asked the question?


=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

(OP)
electricpete,

I have solved part of this problem by carrying a pocket knife with a bottle opener, and by not buying beer with twist-off caps. I am a beer snob. I prefer micro-breweries, especially if they are in walking distance of where I live.

--
JHG

RE: The alligator eats the big number

I think I inadvertently revealed my vulgar taste in beer.

A beer connoisseur, I ain't.

I won't admit to drinking Bud... but Blue Moon with a slice of orange is nice.

=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

I also prefer beer that doesn't have twist-off caps, which is why I generally drink Stella and/or Heineken, as they're bottled overseas and thus have the older style lift-off caps.

John R. Baker, P.E. (ret)
EX-'Product Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: The alligator eats the big number

From a newspaper...


The newspaper says the answer is 5... go figgure?ponder

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

I got caught... although the answers are 120 and 5... the pHD guy answers 5!, which is also 120. The allowable answers do not show 5!.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

I am reminded the "F" in PEMDAS covers this contingency.

RE: The alligator eats the big number

That's like there is no F in DONUTS...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

Interesting reply. Feel any better?

RE: The alligator eats the big number

Almost never feel bad... it's just the imp coming out...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

I am confused by the last 5 or 6 posts.

230 - 220 / 2 .... PEMDAS tells me 120 (230-110), just like dik said 21 Sep 21 19:36.

Then my confusion started with dik's post 22 Sep 21 02:10

> I got caught...

In what way? I thought 120 was right.

> although the answers are 120 and 5... the pHD guy answers 5!, which is also 120.

How is 5 also 120?

> The allowable answers do not show 5!

5 is an allowable answer on the graphic posted 21 Sep 21 19:36. But why do you want it as an allowable answer?

> I am reminded the "F" in PEMDAS covers this contingency.

wut?





=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

Quote (How is 5 also 120?)


I missed it... the exclamation mark is 5 factorial which is 120 (5x4x3x2x1). Fortunately the permissable answers did not include the '!' mark, but the question did.

Quote ("F" in PEMDAS covers this contingency.)


was humour... that's why I added the DONUT comment... readingDave started it.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

Haha, thanks I got it now.

I like it. That's a pretty sly setup. One can easily interpret the ! as exclamation as posted, rather than interpretting it as factorial. Now I see why you said the allowable choices 120 and 5 (not 5!) further obscure the situation....

Someone had to set up those numbers pretty carefully so that the two answers resulting from two choices of OoO (PE-MD-AS or PE-AS-MD) are related to each other through a factorial. That didn't happen by accident! (good thing "accident" isn't a number, I don't have to clarify my meaning).



=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

I'm sure DONOUT is humorous; not related as far as I can tell.

RE: The alligator eats the big number

There is no F in DONUT... they're all gone.

pete... I don't know if it was intentional...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

RE: The alligator eats the big number

It must be a local joke.

RE: The alligator eats the big number

> pete... I don't know if it was intentional...

I dunno. It's not like you can pick some random expression like
2 x 22-20
or
-714+717 x 2
...and expect the right OoO to yield an answer which is the factorial of the answer you'd get from applying the wrong OoO.

Right?

oh, wait...
I know a phd who said the answer to the first is 4!
And the answer to the second was 6!

Maybe I succeeded in undermining my own point.

=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

-40312 + 40316 x 2 = 8!
-3628790 + 3628795 x 2 = 10!

Sorry, now that I finally got the joke, I just can't stop.
The 6!, 8!, 10! all follow the same pattern, I could keep going with the same approach with even integer factorials ad infinitum.
But I admit it's not quite as funny the 4th and 5th time (and when you have to get out your computer / calculator to figure it out!)

=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

Yes, the alligator eats the bigger number, and it helps kiddos remember the difference. ... Two dots always face the bigger number and one dot always faces the smaller number, because two dots are bigger than one dot.
Apart from this if you want to learn something new then the DevOps course will boost your knowledge.

RE: The alligator eats the big number

Shouldn't that be

Quote:

A math PhD says it is 5!.

My glass has a v/c ratio of 0.5

Maybe the tyranny of Murphy is the penalty for hubris. - http://xkcd.com/319/

RE: The alligator eats the big number

The way I was taught about the greater than and less than symbols was the greater than symbol represents the right elbow since the right arm of the body is in most cases stronger than the left arm which is represented by the less than symbol. Once you are taught this statement , you'll never forget the meaning of those two symbols "> and <".






RE: The alligator eats the big number

"Allowable answers" are the solutions to problems of those that live in the alternate reality space.
It's 120.

RE: The alligator eats the big number

Quote (ACtrafficengr)

Maybe the tyranny of Murphy is the penalty for hubris. - http://xkcd.com/319/

Maybe 'penalty for hubris' is just a moralistic way of describing entropy.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

RE: The alligator eats the big number

I look for any excuse to use words like 'splunk', it's just so amusing.
Hey wait a minute, is this SPAM?

Reported.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

RE: The alligator eats the big number

(OP)
ironic metallurgist,

"Splunk" or "Spelunk"? I use the word "nutate" whenever I can.

--
JHG

RE: The alligator eats the big number

Spam, Spam, Spam, Spam...

It was hilarious on Monty Python

... but not so much on eng-tips.

Reported Ankita Garg post 20 May 22 15:58

=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

One man's spam is another man's most important food group...

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

RE: The alligator eats the big number

I'm intrigued as to why a thread on the meaning of the "less than" and "greater than" symbols can run for so long on an Engineering forum?!

Where is the corresponding debate on how to remember the meanings of all the other symbols used in algebra, such as
+ - / (or ÷ if you prefer) × ∞ ≠ ≈ ± ∫ ∑ √
and so on.

Surely < and > are just two more - if you can handle the rest, these two shouldn't give you any trouble!

http://julianh72.blogspot.com

RE: The alligator eats the big number

When I review vendor documents all day long I am doing more than technical reviewing. I am doing their technical work for them because they did not hire me 5 or 15 years ago, and I am teaching remedial English at the grade 8 level.
It's like being punished twice, for something I didn't do.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

RE: The alligator eats the big number

(OP)
jhardy1,

I was amused by the analogy.

--
JHG

RE: The alligator eats the big number

I was helping the daughter of my wife's homecare giver with her Grade 12 math, and had a *.pdf copy of her textbook...

RE: The alligator eats the big number

Quote:

I'm intrigued as to why a thread on the meaning of the "less than" and "greater than" symbols can run for so long on an Engineering forum?!
I doubt anyone here has trouble with it, but that doesn't mean it's not a topic for conversation. We're engineers after all, sometimes known for taking an interest in what others might consider mundane!

Quote:

Surely < and > are just two more - if you can handle the rest, these two shouldn't give you any trouble!

In all seriousness, if someone is troubled by dyslexia, then it's probably a lot easier for them to mix up > vs < than it is for them to mix up + vs - or x vs ÷.

I assume such person would not end up an engineer, but certainly an engineer might be a parent or grandparent of such person, or maybe work with craftspeople who might have such difficulties.

=====================================
(2B)+(2B)' ?

RE: The alligator eats the big number

Quote:

I assume such person would not end up an engineer,

I actually have at least a couple of engineer coworkers that are(were) dyslexic. Had a manager once that managed to check chip layouts, done in colored lines, even though he was totally color blind.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

RE: The alligator eats the big number

Never used the alligator "trick" for > and < ?

The symbol represents a(hungry) alligator's mouth, that will eat the biggest number. If he can choose between 6 and 8, he'll eat the 8. 6 < 8 ; 8 > 6

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