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What's the rule regarding 'ones' in algebra?



 
 
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  #11  
Old September 22nd 03 posted to sci.physics,alt.sci.physics
ghytrfvbnmju7654
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Posts: 409
Default What's the rule regarding 'ones' in algebra?

"Donald G. Shead" wrote in message om...
"Mark Mallory" wrote in message
...


Chergarj wrote:

Can you use ones [1's] indescriminately in algebra? If not why not...



You could, but you would either be wasteful in your steps, or wrong in

your
steps, depending on the context of your quantitative endeaver.

Was that question serious?


Yes it is serious: Many years ago I overheard a H.S. algebra teacher tell
his class _something to the effect_ that the number one [1] was such that it
didn't change the value (of an equation) when it was inserted in an
equation. That made a lasting impression, since I didn't understand then,
and don't now:


If you multiply 1 by something in the equation, it will
not change the meaning of the equation, because any number
multiplied by 1 is still the same number. For example,

xy - st^2 = sx + 3 + sqrt(y-456)

is the same as

1xy - 1st^2 = 1sx + 1*3 + 1sqrt(1y-1*456)

This is probably the wrong newsgroup to be asking math
questions. Future math questions, unless they relate
directly to physics, should probably be posted to
sci.math.
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  #12  
Old September 23rd 03 posted to sci.physics,alt.sci.physics
Double-A
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Posts: 1,658
Default What's the rule regarding 'ones' in algebra?

"Donald G. Shead" wrote in message om...
"Mark Mallory" wrote in message
...


Chergarj wrote:

Can you use ones [1's] indescriminately in algebra? If not why not...



You could, but you would either be wasteful in your steps, or wrong in

your
steps, depending on the context of your quantitative endeaver.

Was that question serious?


Yes it is serious: Many years ago I overheard a H.S. algebra teacher tell
his class _something to the effect_ that the number one [1] was such that it
didn't change the value (of an equation) when it was inserted in an
equation. That made a lasting impression, since I didn't understand then,
and don't now:

In particular: Writing that acceleration [a] is _inversely_ proportional to
the mass [m] of a body, as [a is proportional to 1/m]. That somehow doesn't
look 'copesthetic' to me; especially if 'm' is a variable.


I think you've just about got it.

You can multiply or divide any term or variable in an equation by 1
and still keep the equation in balance.

In your paricular case, if you have

a = F/m

then multiplying the variable F by 1 we have

a = (F*1)/m

which is the same as

a = F * 1/m

so a is directly proportional to F and inversely proportional to m.

Double-A
  #13  
Old September 23rd 03 posted to alt.sci.physics,sci.physics
jmfbahciv@aol.com
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Posts: 7,899
Default What's the rule regarding 'ones' in algebra?

In article ,
"Constantine" wrote:

"Paul Cardinale" wrote in message
m...
"Donald G. Shead" wrote in message

. com...
Can you use ones [1's] indescriminately in algebra? If not why not...


Yes, of course. For example, start with: a + b = c, then we can put
in as many ones as we like: a + b + 1 + 1 + 1 + 1 ... = c. You can be
as indiscriminate as you like with the ones, and you'll be as right as
you always are.


Please, tell me that this was a joke...


GRIN Read the last phrase "you'll be as right as you always
are". Now, consider the fact that he's wrong 100% of the time.

/BAH

Subtract a hundred and four for e-mail.
  #14  
Old September 23rd 03 posted to alt.sci.physics,sci.physics
Paul Cardinale
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Posts: 2,036
Default What's the rule regarding 'ones' in algebra?

"Constantine" wrote in message ...
"Paul Cardinale" wrote in message
...
"Donald G. Shead" wrote in message

om...
Can you use ones [1's] indescriminately in algebra? If not why not...


Yes, of course. For example, start with: a + b = c, then we can put
in as many ones as we like: a + b + 1 + 1 + 1 + 1 ... = c. You can be
as indiscriminate as you like with the ones, and you'll be as right as
you always are.


Please, tell me that this was a joke...

Kostas.


The first two sentences are sarcastic in the extreme. The third is an
accurate statement (when applied to the OP).
Perhaps you need to boost the sensitivity of your sarcasm meter.

Paul Cardinale
  #15  
Old September 23rd 03 posted to alt.sci.physics,sci.physics
Paul Cardinale
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Posts: 2,036
Default What's the rule regarding 'ones' in algebra?

"Donald G. Shead" wrote in message ...
"Constantine" wrote in message
...

"Paul Cardinale" wrote in message
...
"Donald G. Shead" wrote in message

om...
Can you use ones [1's] indescriminately in algebra? If not why not...

Yes, of course. For example, start with: a + b = c, then we can put
in as many ones as we like: a + b + 1 + 1 + 1 + 1 ... = c. You can be
as indiscriminate as you like with the ones, and you'll be as right as
you always are.


Please, tell me that this was a joke...

Kostas.


'Fess-up Paul: That you did it because you are scared as all get out that
Shead's simplicity will upset the applecart: Maybe even shake-up the
gravyboat and a few gravytrains too(:-)


We are as afraid of you as we are of mosquitoes (and we respect you as much).

Psul Cardinale
 




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