info
Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
If x+y=z, is x+y-z=0?
38 views
Skip to first unread message
Chong Chin Herng
Feb 4, 2017, 9:00:00 AM2/4/17
to
What I did is I moved z to the left hand side.
Barb Knox
Feb 4, 2017, 2:43:51 PM2/4/17
to
On 5/02/2017 00:35, Chong Chin Herng wrote:
> What I did is I moved z to the left hand side.
Is that current eduspeak for "Subtract z from both sides"?
> What I did is I moved z to the left hand side.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | ,008015L080180,022036,029037
| B B a a r b b | ,047045,L014114L4.
| BBB aa a r bbb |
-----------------------------
Arturo Magidin
Feb 4, 2017, 6:01:04 PM2/4/17
to
On Saturday, February 4, 2017 at 1:43:51 PM UTC-6, Barb Knox wrote:
> On 5/02/2017 00:35, Chong Chin Herng wrote:
> > What I did is I moved z to the left hand side.
>
> Is that current eduspeak for "Subtract z from both sides"?
Well, if it is "current", it is consonant with the way it was said right before and right after "new math", which was the first which explicitly talked about the underlying algebraic theory instead of just the skill.
> On 5/02/2017 00:35, Chong Chin Herng wrote:
> > What I did is I moved z to the left hand side.
>
> Is that current eduspeak for "Subtract z from both sides"?
--
Arturo Magidin
Barb Knox
Feb 5, 2017, 1:18:56 PM2/5/17
to
much *less* algebraic content than the notion of applying the same
function to both sides of an equality, which (IMO) is why the OP didn't
immediately see that it produces a correct answer. Knowing when to
"move" terms is purely a rote mechanical skill, not an understanding of
algebraic theory.
I'd like to ask the OP:
Did recasting the operation as subtracting z from both sides make the
answer obvious to you?
BTW, I did school mathematics just before New Math came in, and didn't
encounter mindless moving of terms divorced from any algebraic content.
Michael F. Stemper
Feb 5, 2017, 6:48:53 PM2/5/17
to
On 2017-02-04 05:35, Chong Chin Herng wrote:
> What I did is I moved z to the left hand side.
Copying the question from the subject line to where it belongs;
> What I did is I moved z to the left hand side.
If x+y=z, is x+y-z = 0?
Let's start with what we know to be true:
x + y = z
What does this mean? That's really the most important question
here. The equals sign "=" means that x+y and z are the same thing,
just represented differently. Since they're the same thing, if we
add something to both of them, the results will be the same.
They will not be the same as before, since we've added something
to them, but they'll still be the same as each other. For instance
we can add -z to both sides, and get:
x + y + (-z) = z + (-z)
Since adding -z is the same as subtracting z, we can rewrite the
left-hand side, giving us:
x + y - z = z + (-z)
Let's look at the right-hand side next. What is -z? It's the number
that, when you add it to z, gives 0. In other words:
z + (-z) = 0
Since z + (-z) is the same as 0, we can replace one for the other,
giving us:
x + y - z = 0
Hopefully, this helps you see what was done and, more importantly,
why each step is correct.
--
Michael F. Stemper
Indians scattered on dawn's highway bleeding;
Ghosts crowd the young child's fragile eggshell mind.
Arturo Magidin
Feb 5, 2017, 7:56:03 PM2/5/17
to
On Sunday, February 5, 2017 at 12:18:56 PM UTC-6, Barb Knox wrote:
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
I did it just during and right after, and right after I did.
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
--
Arturo Magidin
Stan Brown
Feb 5, 2017, 10:22:41 PM2/5/17
to
On Mon, 6 Feb 2017 07:18:51 +1300, Barb Knox wrote:
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality,
>
Hear, hear! (I'd probably say "operation" rather than "function",
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality,
>
but that's a minor quibble. I absolutely agree with the main point.)
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://BrownMath.com/
http://OakRoadSystems.com/
Shikata ga nai...
Stan Brown
Feb 5, 2017, 10:23:31 PM2/5/17
to
On Sun, 5 Feb 2017 17:48:41 -0600, Michael F. Stemper wrote:
>
> On 2017-02-04 05:35, Chong Chin Herng wrote:
> > What I did is I moved z to the left hand side.
>
> Copying the question from the subject line to where it belongs;
>
> If x+y=z, is x+y-z = 0?
Funny coincidence: there's a thread on this exact topic in
>
> On 2017-02-04 05:35, Chong Chin Herng wrote:
> > What I did is I moved z to the left hand side.
>
> Copying the question from the subject line to where it belongs;
>
> If x+y=z, is x+y-z = 0?
alt.algebra.help.
Nick
Feb 6, 2017, 4:38:58 PM2/6/17
to
On 05/02/2017 18:18, Barb Knox wrote:
> On 5/02/2017 12:01, Arturo Magidin wrote:
>> On Saturday, February 4, 2017 at 1:43:51 PM UTC-6, Barb Knox wrote:
>>> On 5/02/2017 00:35, Chong Chin Herng wrote:
>>>> What I did is I moved z to the left hand side.
>
>>> Is that current eduspeak for "Subtract z from both sides"?
>
>> Well, if it is "current", it is consonant with the way it was said
>> right before and right after "new math", which was the first which
>> explicitly talked about the underlying algebraic theory instead of
>> just the skill.
>
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality, which (IMO) is why the OP didn't
> immediately see that it produces a correct answer. Knowing when to
> "move" terms is purely a rote mechanical skill, not an understanding of
> algebraic theory.
>
> I'd like to ask the OP:
> Did recasting the operation as subtracting z from both sides make the
> answer obvious to you?
>
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
>
>
It seems to me that if x,y,z are elements of a group the question can be
> On 5/02/2017 12:01, Arturo Magidin wrote:
>> On Saturday, February 4, 2017 at 1:43:51 PM UTC-6, Barb Knox wrote:
>>> On 5/02/2017 00:35, Chong Chin Herng wrote:
>>>> What I did is I moved z to the left hand side.
>
>>> Is that current eduspeak for "Subtract z from both sides"?
>
>> Well, if it is "current", it is consonant with the way it was said
>> right before and right after "new math", which was the first which
>> explicitly talked about the underlying algebraic theory instead of
>> just the skill.
>
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality, which (IMO) is why the OP didn't
> immediately see that it produces a correct answer. Knowing when to
> "move" terms is purely a rote mechanical skill, not an understanding of
> algebraic theory.
>
> I'd like to ask the OP:
> Did recasting the operation as subtracting z from both sides make the
> answer obvious to you?
>
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
>
>
answered by mechanically applying group axioms.
I did new math, I liked it well enough. I didn't do abstract algebra
until university. It all seemed to fit together well enough.
Do students get group theory at school now?
Nick
Feb 6, 2017, 4:44:34 PM2/6/17
to
On 06/02/2017 03:22, Stan Brown wrote:
> On Mon, 6 Feb 2017 07:18:51 +1300, Barb Knox wrote:
>> What prompted my post is that the notion of "moving" terms around has
>> much *less* algebraic content than the notion of applying the same
>> function to both sides of an equality,
>>
>
> Hear, hear! (I'd probably say "operation" rather than "function",
> but that's a minor quibble. I absolutely agree with the main point.)
>
I prefer function, simpler. Although I kind of knew that an operation
> On Mon, 6 Feb 2017 07:18:51 +1300, Barb Knox wrote:
>> What prompted my post is that the notion of "moving" terms around has
>> much *less* algebraic content than the notion of applying the same
>> function to both sides of an equality,
>>
>
> Hear, hear! (I'd probably say "operation" rather than "function",
> but that's a minor quibble. I absolutely agree with the main point.)
>
was a function I still need to look it up to be sure.
Stan Brown
Feb 7, 2017, 7:02:02 AM2/7/17
to
sides, but I'm forced to agree that subtracting the same quantity
from both sides is equally a function: f(u) = u - z.
Michael F. Stemper
Feb 7, 2017, 9:40:00 AM2/7/17
to
On 2017-02-05 21:23, Stan Brown wrote:
> On Sun, 5 Feb 2017 17:48:41 -0600, Michael F. Stemper wrote:
>>
>> On 2017-02-04 05:35, Chong Chin Herng wrote:
>>> What I did is I moved z to the left hand side.
>>
>> Copying the question from the subject line to where it belongs;
>>
>> If x+y=z, is x+y-z = 0?
>
> Funny coincidence: there's a thread on this exact topic in
> alt.algebra.help.
Multi-posted? Tsk, tsk.
> On Sun, 5 Feb 2017 17:48:41 -0600, Michael F. Stemper wrote:
>>
>> On 2017-02-04 05:35, Chong Chin Herng wrote:
>>> What I did is I moved z to the left hand side.
>>
>> Copying the question from the subject line to where it belongs;
>>
>> If x+y=z, is x+y-z = 0?
>
> Funny coincidence: there's a thread on this exact topic in
> alt.algebra.help.
Did the OP reply to any of the followups there?
--
Michael F. Stemper
Economists have correctly predicted seven of the last three recessions.
Peter Percival
Feb 8, 2017, 12:56:54 PM2/8/17
to
Barb Knox wrote:
> On 5/02/2017 12:01, Arturo Magidin wrote:
>> On Saturday, February 4, 2017 at 1:43:51 PM UTC-6, Barb Knox wrote:
>>> On 5/02/2017 00:35, Chong Chin Herng wrote:
>>>> What I did is I moved z to the left hand side.
>
>>> Is that current eduspeak for "Subtract z from both sides"?
>
>> Well, if it is "current", it is consonant with the way it was said
>> right before and right after "new math", which was the first which
>> explicitly talked about the underlying algebraic theory instead of
>> just the skill.
>
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality, which (IMO) is why the OP didn't
> immediately see that it produces a correct answer. Knowing when to
> "move" terms is purely a rote mechanical skill, not an understanding of
> algebraic theory.
>
> I'd like to ask the OP:
> Did recasting the operation as subtracting z from both sides make the
> answer obvious to you?
>
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
>
I remember the mantra "change the side, change the sign"! I don't
> On 5/02/2017 12:01, Arturo Magidin wrote:
>> On Saturday, February 4, 2017 at 1:43:51 PM UTC-6, Barb Knox wrote:
>>> On 5/02/2017 00:35, Chong Chin Herng wrote:
>>>> What I did is I moved z to the left hand side.
>
>>> Is that current eduspeak for "Subtract z from both sides"?
>
>> Well, if it is "current", it is consonant with the way it was said
>> right before and right after "new math", which was the first which
>> explicitly talked about the underlying algebraic theory instead of
>> just the skill.
>
> What prompted my post is that the notion of "moving" terms around has
> much *less* algebraic content than the notion of applying the same
> function to both sides of an equality, which (IMO) is why the OP didn't
> immediately see that it produces a correct answer. Knowing when to
> "move" terms is purely a rote mechanical skill, not an understanding of
> algebraic theory.
>
> I'd like to ask the OP:
> Did recasting the operation as subtracting z from both sides make the
> answer obvious to you?
>
> BTW, I did school mathematics just before New Math came in, and didn't
> encounter mindless moving of terms divorced from any algebraic content.
>
recall if it had any algebraic underpinning.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Cage, John
Feb 14, 2017, 10:20:01 PM2/14/17
to
It's clearly that x+y-z=0!
Todd Hicks
Feb 15, 2017, 7:50:01 AM2/15/17
to
It's hard to solve this without knowing what x, y and z are.
Barb Knox
Feb 15, 2017, 2:29:54 PM2/15/17
to
On 16/02/2017 00:54, Todd Hicks wrote:
> It's hard to solve this without knowing what x, y and z are.
Please explain.
> It's hard to solve this without knowing what x, y and z are.
Barb Knox
Feb 15, 2017, 2:33:39 PM2/15/17
to
On 15/02/2017 15:08, Cage, John wrote:
> It's clearly [true] that x+y-z=0!
Not to everyone, e.g. the OP.
> It's clearly [true] that x+y-z=0!
Not to everyone, e.g. the OP.
Nick
Feb 16, 2017, 10:00:15 AM2/16/17
to
On 15/02/2017 19:29, Barb Knox wrote:
> On 16/02/2017 00:54, Todd Hicks wrote:
>> It's hard to solve this without knowing what x, y and z are.
>
> Please explain.
>
>
I would need to know that x,y,z are elements of a group with the group
> On 16/02/2017 00:54, Todd Hicks wrote:
>> It's hard to solve this without knowing what x, y and z are.
>
> Please explain.
>
>
operation +.
Barb Knox
Feb 16, 2017, 3:01:52 PM2/16/17
to
operation "+" then there would not also be an operation "-".
(Group problems generally have operations "*" and superscript "-1". And
the identity is generally "1", not "0".)
This is just a *school* algebra problem, over numbers.
(It's another question why it was originally posted to
alt.math.undergrad. Maybe it's for a remedial class.)
Peter Percival
Feb 16, 2017, 3:57:50 PM2/16/17
to
Barb Knox wrote:
> On 17/02/2017 04:00, Nick wrote:
>> On 15/02/2017 19:29, Barb Knox wrote:
>>> On 16/02/2017 00:54, Todd Hicks wrote:
>>>> It's hard to solve this without knowing what x, y and z are.
>
>>> Please explain.
>
>
>> I would need to know that x,y,z are elements of a group with the group
>> operation +.
>
> You are confused. If it were an abstract-algebra group problem with
> operation "+" then there would not also be an operation "-".
? Binary - would usually be a defined operation.
> On 17/02/2017 04:00, Nick wrote:
>> On 15/02/2017 19:29, Barb Knox wrote:
>>> On 16/02/2017 00:54, Todd Hicks wrote:
>>>> It's hard to solve this without knowing what x, y and z are.
>
>>> Please explain.
>
>
>> I would need to know that x,y,z are elements of a group with the group
>> operation +.
>
> You are confused. If it were an abstract-algebra group problem with
> operation "+" then there would not also be an operation "-".
>
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".)
>
> This is just a *school* algebra problem, over numbers.
>
> (It's another question why it was originally posted to
> alt.math.undergrad. Maybe it's for a remedial class.)
>
>
--
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".)
>
> This is just a *school* algebra problem, over numbers.
>
> (It's another question why it was originally posted to
> alt.math.undergrad. Maybe it's for a remedial class.)
>
>
--
Nick
Feb 16, 2017, 5:24:20 PM2/16/17
to
On 16/02/2017 20:01, Barb Knox wrote:
> On 17/02/2017 04:00, Nick wrote:
>> On 15/02/2017 19:29, Barb Knox wrote:
>>> On 16/02/2017 00:54, Todd Hicks wrote:
>>>> It's hard to solve this without knowing what x, y and z are.
>
>>> Please explain.
>
>
>> I would need to know that x,y,z are elements of a group with the group
>> operation +.
>
> You are confused. If it were an abstract-algebra group problem with
> operation "+" then there would not also be an operation "-".
>
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".)
>
> This is just a *school* algebra problem, over numbers.
>
> (It's another question why it was originally posted to
> alt.math.undergrad. Maybe it's for a remedial class.)
>
OK apologies.
> On 17/02/2017 04:00, Nick wrote:
>> On 15/02/2017 19:29, Barb Knox wrote:
>>> On 16/02/2017 00:54, Todd Hicks wrote:
>>>> It's hard to solve this without knowing what x, y and z are.
>
>>> Please explain.
>
>
>> I would need to know that x,y,z are elements of a group with the group
>> operation +.
>
> You are confused. If it were an abstract-algebra group problem with
> operation "+" then there would not also be an operation "-".
>
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".)
>
> This is just a *school* algebra problem, over numbers.
>
> (It's another question why it was originally posted to
> alt.math.undergrad. Maybe it's for a remedial class.)
>
I must admit school math always confused me with a bunch of assumptions
I was supposed to know about but I never quite knew where they were
defined. Hence I found them very difficult. I've always had attention
problems so I probably wasn't listening when I was supposed to.
Fortunately things got much easier at university.
Peter Percival
Feb 18, 2017, 10:41:59 PM2/18/17
to
Barb Knox wrote:
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".
For abelian groups additive notation is common.
> (Group problems generally have operations "*" and superscript "-1". And
> the identity is generally "1", not "0".
Ah Zong
Dec 4, 2021, 1:42:54 AM12/4/21
to
My friend searched my name on Google and managed to find this post which I've forgot about. I would like to thank everyone who have answered. I want to point out that indeed my school had taught me to "subtract z from both sides" but I wasn't paying attention. They then assumed we had such notion and started saying "moving z to the left hand side".
I'm graduating high school in less than one month and my final advanced mathematics exam is in one week. Mathematics has become my favourite subject and one of the subjects which I excel in. This post truly brought me memories. Can't believe that I went from this post to taking part in math olympiads to mastering high school calculus. Time flies.
I'm graduating high school in less than one month and my final advanced mathematics exam is in one week. Mathematics has become my favourite subject and one of the subjects which I excel in. This post truly brought me memories. Can't believe that I went from this post to taking part in math olympiads to mastering high school calculus. Time flies.
0 new messages