# OT: Those arithmetic questions

Started by January 23, 2018
```On 02/02/18 22:29, Les Cargill wrote:
> Steve Underwood wrote:
>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>> Sure, it's not what we know that I am commenting about though, it is how
>>>>> kids at school are taught
>>>>>
>>>>>
>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>
>>>>>
>>>>>
>>>> As in a lot of the discussions on this topic, I see that article refer to
>>>> PEMDAS. Its usually described as something pretty old, that all school kids
>>>> are taught. Was anyone here taught PEMDAS? I certainly wasn't.
>>>
>>> I, and everyone else of my age, was taught BEDMAS, which is the same thing.
>>> That's not to say everyone remembered it. Even teachers can and do think
>>> 1+2*3 is 9.
>>
>> I just asked my children, who are 18 and 20. They had never heard of PEMDAS or
>> BEDMAS as mnemonics. They do, however, know that 1+2*3 is 7. Its just division
>> that makes things woolly.
>>
>> Steve
>>
>
> 1+2*3 with a classic stack-based Push Down Automata
> algebraic calculator will yield 9. So I'd say it is
> *at best* ambiguous.

No, the correct answer to 1+2*3 is not ambiguous.

A calculator used as you describe is calculating
(1+2)*3, whether or not the operator realises it.

The relationship between computer arithmetic and
"maths" arithmetic is tenuous at best, and you need
to understand the specific language (as well as
the underlying representation's weaknesses). For
example there is at least one influential computer
language where
7 - 7 is 0
7 - 7 - 7 is 7
7 - 7 - 7 - 7 is 0
7 - 7 - 7 - 7 -7 is 7
Have a go with that http://tryapl.org/:)
```
```Tom Gardner wrote:
> On 02/02/18 22:29, Les Cargill wrote:
>> Steve Underwood wrote:
>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>> Sure, it's not what we know that I am commenting about though, it
>>>>>> is how
>>>>>> kids at school are taught
>>>>>>
>>>>>>
>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>
>>>>>>
>>>>>>
>>>>> As in a lot of the discussions on this topic, I see that article
>>>>> refer to
>>>>> PEMDAS. Its usually described as something pretty old, that all
>>>>> school kids
>>>>> are taught. Was anyone here taught PEMDAS? I certainly wasn't.
>>>>
>>>> I, and everyone else of my age, was taught BEDMAS, which is the same
>>>> thing.
>>>> That's not to say everyone remembered it. Even teachers can and do
>>>> think
>>>> 1+2*3 is 9.
>>>
>>> I just asked my children, who are 18 and 20. They had never heard of
>>> PEMDAS or
>>> BEDMAS as mnemonics. They do, however, know that 1+2*3 is 7. Its just
>>> division
>>> that makes things woolly.
>>>
>>> Steve
>>>
>>
>> 1+2*3 with a classic stack-based Push Down Automata
>> algebraic calculator will yield 9. So I'd say it is
>> *at best* ambiguous.
>
> No, the correct answer to 1+2*3 is not ambiguous.
>
> A calculator used as you describe is calculating
> (1+2)*3, whether or not the operator realises it.
>

You're implying precedence of "*" over "+". Post hoc or

All I am required to do to refute that is provide a single
counterexample.

--
Les Cargill
```
```On 03/02/18 03:43, Les Cargill wrote:
> Tom Gardner wrote:
>> On 02/02/18 22:29, Les Cargill wrote:
>>> Steve Underwood wrote:
>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>>> Sure, it's not what we know that I am commenting about though, it is how
>>>>>>> kids at school are taught
>>>>>>>
>>>>>>>
>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> As in a lot of the discussions on this topic, I see that article refer to
>>>>>> PEMDAS. Its usually described as something pretty old, that all school kids
>>>>>> are taught. Was anyone here taught PEMDAS? I certainly wasn't.
>>>>>
>>>>> I, and everyone else of my age, was taught BEDMAS, which is the same thing.
>>>>> That's not to say everyone remembered it. Even teachers can and do think
>>>>> 1+2*3 is 9.
>>>>
>>>> I just asked my children, who are 18 and 20. They had never heard of PEMDAS or
>>>> BEDMAS as mnemonics. They do, however, know that 1+2*3 is 7. Its just division
>>>> that makes things woolly.
>>>>
>>>> Steve
>>>>
>>>
>>> 1+2*3 with a classic stack-based Push Down Automata
>>> algebraic calculator will yield 9. So I'd say it is
>>> *at best* ambiguous.
>>
>> No, the correct answer to 1+2*3 is not ambiguous.
>>
>> A calculator used as you describe is calculating
>> (1+2)*3, whether or not the operator realises it.
>>
>
>
> You're implying precedence of "*" over "+". Post hoc or

I'm not implying anything. I'm merely stating the
long established rules of maths.

> All I am required to do to refute that is provide a single
> counterexample.

Don't be silly.

"I have a calculator that says 1+2*3 is 0, therefore that's
what it is". Ahem.

```
```On 02/03/2018 09:24 AM, Tom Gardner wrote:
> On 03/02/18 03:43, Les Cargill wrote:
>> Tom Gardner wrote:
>>> On 02/02/18 22:29, Les Cargill wrote:
>>>>
>>>> 1+2*3 with a classic stack-based Push Down Automata
>>>> algebraic calculator will yield 9. So I'd say it is
>>>> *at best* ambiguous.
>>>
>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>
>>> A calculator used as you describe is calculating
>>> (1+2)*3, whether or not the operator realises it.
>>>
>>
>>
>> You're implying precedence of "*" over "+". Post hoc or
>
> I'm not implying anything. I'm merely stating the
> long established rules of maths.
>
>
>> All I am required to do to refute that is provide a single
>> counterexample.
>
> Don't be silly.
>
> "I have a calculator that says 1+2*3 is 0, therefore that's
> what it is". Ahem.
>

There is a YouTube video (which I can't find at the moment) where they
enter one of these "problematic" expressions into several models of
Casio calculators, all approved for school or college use in various
places. Even the models from a single maker didn't agree on the answer.

Regards,
Steve
```
```On 03/02/18 12:55, Steve Underwood wrote:
> On 02/03/2018 09:24 AM, Tom Gardner wrote:
>> On 03/02/18 03:43, Les Cargill wrote:
>>> Tom Gardner wrote:
>>>> On 02/02/18 22:29, Les Cargill wrote:
>>>>>
>>>>> 1+2*3 with a classic stack-based Push Down Automata
>>>>> algebraic calculator will yield 9. So I'd say it is
>>>>> *at best* ambiguous.
>>>>
>>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>>
>>>> A calculator used as you describe is calculating
>>>> (1+2)*3, whether or not the operator realises it.
>>>>
>>>
>>>
>>> You're implying precedence of "*" over "+". Post hoc or
>>
>> I'm not implying anything. I'm merely stating the
>> long established rules of maths.
>>
>>
>>> All I am required to do to refute that is provide a single
>>> counterexample.
>>
>> Don't be silly.
>>
>> "I have a calculator that says 1+2*3 is 0, therefore that's
>> what it is". Ahem.
>>
>
> There is a YouTube video (which I can't find at the moment) where they enter one
> of these "problematic" expressions into several models of Casio calculators, all
> approved for school or college use in various places. Even the models from a
> single maker didn't agree on the answer.

Just so. Indeed I've been able to demonstrate that with Casio calculators
to my daughter - as a cautionary tale of not trusting equipment but learning how
to use it.

But that has zero effect on the laws of arithmetic.

```
```On Saturday, February 3, 2018 at 3:07:16 AM UTC+13, Tom Gardner wrote:
> On 02/02/18 10:07, Steve Underwood wrote:
> > On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
> >> Sure, it's not what we know that I am commenting about though, it is how
> >> kids at school are taught
> >>
> >>
> >> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
> >>
> >>
> >>
> > As in a lot of the discussions on this topic, I see that article refer to
> > PEMDAS. Its usually described as something pretty old, that all school kids
> > are taught. Was anyone here taught PEMDAS? I certainly wasn't.
>
> I, and everyone else of my age, was taught BEDMAS, which is the same thing.
> That's not to say everyone remembered it. Even teachers can and do think 1+2*3 is 9.
>
>
> > I've always read a / as pretty much "put the stuff to the left of the '/'
> > over the stuff to the right of it", which is definitely not what PEMDAS says.
> > Most of what has been written actually uses the traditional divide symbol,
> > rather than a slash, but some writers are using / and the traditional divide
> > symbol completely interchangeably.
>
> So what? It is your right to be wrong :)
>
>
> > At the end of the day, anyone writing expressions for consumption by others
> > should never be too conservative about the liberal use of parentheses.
>
> Anyone confusing arithmetic and computer arithmetic will, sooner rather than
> later, be bitten by that error.

I was schooled in the 60s at a very good school in Scotland and we never used any of that PEDMAs BEDMAS or the like all the time we were there. The reason was that we never got our sums (as we called it, or arithmetic - never maths or math) in a single line. It was written 123 + 456 one above the other or only on a straight line when doing long division. Because the long divisions were pretty complicated with decimal points, there wasn't another addition after it, it was a problem in itself (calculators were not invented then of course for the individual). Later in algebra we learned brackets and the associative, commutative and distributive laws and I suppose most if it became obvious after that. Once on to algebra of course rarely if ever do we see equations written in an ambiguous form, we use fractions and brackets. The only time I had difficulty was when I was about 17 and wrote my first computer program on a mainframe, then  you have to write in a line!! To get round this I always to this day use brackets even when none are needed, just to be extra sure.
```
```Tom Gardner wrote:
> On 03/02/18 03:43, Les Cargill wrote:
>> Tom Gardner wrote:
>>> On 02/02/18 22:29, Les Cargill wrote:
>>>> Steve Underwood wrote:
>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>>>> Sure, it's not what we know that I am commenting about though,
>>>>>>>> it is how
>>>>>>>> kids at school are taught
>>>>>>>>
>>>>>>>>
>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>> As in a lot of the discussions on this topic, I see that article
>>>>>>> refer to
>>>>>>> PEMDAS. Its usually described as something pretty old, that all
>>>>>>> school kids
>>>>>>> are taught. Was anyone here taught PEMDAS? I certainly wasn't.
>>>>>>
>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the
>>>>>> same thing.
>>>>>> That's not to say everyone remembered it. Even teachers can and do
>>>>>> think
>>>>>> 1+2*3 is 9.
>>>>>
>>>>> I just asked my children, who are 18 and 20. They had never heard
>>>>> of PEMDAS or
>>>>> BEDMAS as mnemonics. They do, however, know that 1+2*3 is 7. Its
>>>>> just division
>>>>> that makes things woolly.
>>>>>
>>>>> Steve
>>>>>
>>>>
>>>> 1+2*3 with a classic stack-based Push Down Automata
>>>> algebraic calculator will yield 9. So I'd say it is
>>>> *at best* ambiguous.
>>>
>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>
>>> A calculator used as you describe is calculating
>>> (1+2)*3, whether or not the operator realises it.
>>>
>>
>>
>> You're implying precedence of "*" over "+". Post hoc or
>
> I'm not implying anything. I'm merely stating the
> long established rules of maths.
>
>

I just mean that that's what they told us in junior high school
to keep from having to answer dumb questions as a convention.

I really do mean that "when you read stuff, it depends on the
conventions of the people writing the stuff" and that
the Junior High School version is not a particularly privileged
... example.

>> All I am required to do to refute that is provide a single
>> counterexample.
>
> Don't be silly.
>

Oh, c'mon. There isn't enough silly in the world. :)

> "I have a calculator that says 1+2*3 is 0, therefore that's
> what it is". Ahem.
>

--
Les Cargill
```
```On 05/02/18 23:35, Les Cargill wrote:
> Tom Gardner wrote:
>> On 03/02/18 03:43, Les Cargill wrote:
>>> Tom Gardner wrote:
>>>> On 02/02/18 22:29, Les Cargill wrote:
>>>>> Steve Underwood wrote:
>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>>>>> Sure, it's not what we know that I am commenting about
>>>>>>>>> though, it is how kids at school are taught
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>>
As in a lot of the discussions on this topic, I see that article refer to
>>>>>>>> PEMDAS. Its usually described as something pretty old, that all
>>>>>>>> school kids are taught. Was anyone here taught PEMDAS? I
>>>>>>>> certainly wasn't.
>>>>>>>
>>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the
>>>>>>> same thing. That's not to say everyone remembered it. Even
>>>>>>> teachers can and do think 1+2*3 is 9.
>>>>>>
>>>>>> I just asked my children, who are 18 and 20. They had never heard
>>>>>> of PEMDAS or BEDMAS as mnemonics. They do, however, know that 1+2*3
>>>>>> is 7. Its just division that makes things woolly.
>>>>>>
>>>>>> Steve
>>>>>>
>>>>>
>>>>> 1+2*3 with a classic stack-based Push Down Automata algebraic
>>>>> calculator will yield 9. So I'd say it is *at best* ambiguous.
>>>>
>>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>>
>>>> A calculator used as you describe is calculating (1+2)*3, whether or
>>>> not the operator realises it.
>>>>
>>>
>>>
>>> You're implying precedence of "*" over "+". Post hoc or argumentum ad
>>
>> I'm not implying anything. I'm merely stating the long established rules of
>> maths.
>>
>>
>
> I just mean that that's what they told us in junior high school to keep from
> having to answer dumb questions as a convention.
>
> I really do mean that "when you read stuff, it depends on the conventions of
> the people writing the stuff" and that the Junior High School version is not
> a particularly privileged ... example.

If you really think that, I suggest you have a long
discussion with some mathematicians. That excludes
schoolteachers and most engineers.

>>> All I am required to do to refute that is provide a single
>>> counterexample.
>>
>> Don't be silly.
>>
>
> Oh, c'mon. There isn't enough silly in the world. :)
>
>> "I have a calculator that says 1+2*3 is 0, therefore that's what it is".
>> Ahem.
>>
>

I have highly intelligent distant relatives[1] that refuse
to believe that US astronauts walked on the moon. The moon
landings are all capitalist fake news stories.

[1] as in one has worked with/for Vladimir Putin
```
```On 06/02/18 00:23, Tom Gardner wrote:
> On 05/02/18 23:35, Les Cargill wrote:
>> Tom Gardner wrote:
>>> On 03/02/18 03:43, Les Cargill wrote:
>>>> Tom Gardner wrote:
>>>>> On 02/02/18 22:29, Les Cargill wrote:
>>>>>> Steve Underwood wrote:
>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>>>>>> Sure, it's not what we know that I am commenting about
>>>>>>>>>> though, it is how kids at school are taught
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
> As in a lot of the discussions on this topic, I see that article refer to
>>>>>>>>> PEMDAS. Its usually described as something pretty old, that all
>>>>>>>>> school kids are taught. Was anyone here taught PEMDAS? I
>>>>>>>>> certainly wasn't.
>>>>>>>>
>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the
>>>>>>>> same thing. That's not to say everyone remembered it. Even
>>>>>>>> teachers can and do think 1+2*3 is 9.
>>>>>>>
>>>>>>> I just asked my children, who are 18 and 20. They had never heard
>>>>>>> of PEMDAS or BEDMAS as mnemonics. They do, however, know that 1+2*3
>>>>>>> is 7. Its just division that makes things woolly.
>>>>>>>
>>>>>>> Steve
>>>>>>>
>>>>>>
>>>>>> 1+2*3 with a classic stack-based Push Down Automata algebraic
>>>>>> calculator will yield 9. So I'd say it is *at best* ambiguous.
>>>>>
>>>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>>>
>>>>> A calculator used as you describe is calculating (1+2)*3, whether or
>>>>> not the operator realises it.
>>>>>
>>>>
>>>>
>>>> You're implying precedence of "*" over "+". Post hoc or argumentum ad
>>>
>>> I'm not implying anything. I'm merely stating the long established rules of
>>> maths.
>>>
>>>
>>
>> I just mean that that's what they told us in junior high school to keep from
>> having to answer dumb questions as a convention.
>>
>> I really do mean that "when you read stuff, it depends on the conventions of
>> the people writing the stuff" and that the Junior High School version is not
>> a particularly privileged ... example.
>
> If you really think that, I suggest you have a long
> discussion with some mathematicians. That excludes
> schoolteachers and most engineers.
>
>
>>>> All I am required to do to refute that is provide a single
>>>> counterexample.
>>>
>>> Don't be silly.
>>>
>>
>> Oh, c'mon. There isn't enough silly in the world. :)
>>
>>> "I have a calculator that says 1+2*3 is 0, therefore that's what it is".
>>> Ahem.
>>>
>>
>
> I have highly intelligent distant relatives[1] that refuse
> to believe that US astronauts walked on the moon. The moon
> landings are all capitalist fake news stories.
>
> [1] as in one has worked with/for Vladimir Putin

Drat; that escaped too early.

I intended to note that /clearly/ there is a scientific
debate between people with differing opinions about whether
man landed on the moon or not.
```
```Tom Gardner wrote:
> On 06/02/18 00:23, Tom Gardner wrote:
>> On 05/02/18 23:35, Les Cargill wrote:
>>> Tom Gardner wrote:
>>>> On 03/02/18 03:43, Les Cargill wrote:
>>>>> Tom Gardner wrote:
>>>>>> On 02/02/18 22:29, Les Cargill wrote:
>>>>>>> Steve Underwood wrote:
>>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote:
>>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote:
>>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote:
>>>>>>>>>>> Sure, it's not what we know that I am commenting about
>>>>>>>>>>> though, it is how kids at school are taught
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>
>> As in a lot of the discussions on this topic, I see that article refer to
>>>>>>>>>> PEMDAS. Its usually described as something pretty old, that all
>>>>>>>>>> school kids are taught. Was anyone here taught PEMDAS? I
>>>>>>>>>> certainly wasn't.
>>>>>>>>>
>>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the
>>>>>>>>> same thing. That's not to say everyone remembered it. Even
>>>>>>>>> teachers can and do think 1+2*3 is 9.
>>>>>>>>
>>>>>>>> I just asked my children, who are 18 and 20. They had never heard
>>>>>>>> of PEMDAS or BEDMAS as mnemonics. They do, however, know that 1+2*3
>>>>>>>> is 7. Its just division that makes things woolly.
>>>>>>>>
>>>>>>>> Steve
>>>>>>>>
>>>>>>>
>>>>>>> 1+2*3 with a classic stack-based Push Down Automata algebraic
>>>>>>> calculator will yield 9. So I'd say it is *at best* ambiguous.
>>>>>>
>>>>>> No, the correct answer to 1+2*3 is not ambiguous.
>>>>>>
>>>>>> A calculator used as you describe is calculating (1+2)*3, whether or
>>>>>> not the operator realises it.
>>>>>>
>>>>>
>>>>>
>>>>> You're implying precedence of "*" over "+". Post hoc or argumentum ad
>>>>
>>>> I'm not implying anything. I'm merely stating the long established
>>>> rules of
>>>> maths.
>>>>
>>>>
>>>
>>> I just mean that that's what they told us in junior high school to
>>> keep from
>>> having to answer dumb questions as a convention.
>>>
>>> I really do mean that "when you read stuff, it depends on the
>>> conventions of
>>> the people writing the stuff" and that the Junior High School version
>>> is not
>>> a particularly privileged ... example.
>>
>> If you really think that, I suggest you have a long
>> discussion with some mathematicians. That excludes
>> schoolteachers and most engineers.
>>
>>
>>>>> All I am required to do to refute that is provide a single
>>>>> counterexample.
>>>>
>>>> Don't be silly.
>>>>
>>>
>>> Oh, c'mon. There isn't enough silly in the world. :)
>>>
>>>> "I have a calculator that says 1+2*3 is 0, therefore that's what it
>>>> is".
>>>> Ahem.
>>>>
>>>
>>
>> I have highly intelligent distant relatives[1] that refuse
>> to believe that US astronauts walked on the moon. The moon
>> landings are all capitalist fake news stories.
>>
>> [1] as in one has worked with/for Vladimir Putin
>
> Drat; that escaped too early.
>
> I intended to note that /clearly/ there is a scientific
> debate between people with differing opinions about whether
> man landed on the moon or not.

LOL!

Alls I am saying is that whether or not the expectation that
"multiplication has precedence over addition" will be met will,