Science Forums Biology Forum Molecular Biology Forum Physics Chemistry Forum What's the rule about using 'ones' in algebra?

 Physics Forum Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

# What's the rule about using 'ones' in algebra?

## What's the rule about using 'ones' in algebra? - Physics Forum

### What's the rule about using 'ones' in algebra? - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

#1
09-21-2003, 08:33 PM
 Donald G. Shead Guest Posts: n/a
What's the rule about using 'ones' in algebra?

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

#2
09-21-2003, 09:20 PM
 dlzc@aol.com \(formerly\) Guest Posts: n/a
What's the rule about using 'ones' in algebra?

"Donald G. Shead" <[Only registered users see links. ]> wrote in message
news:QWnbb.4796\$[Only registered users see links. ].prodigy.co m...

They're used in mechanics quite a bit. Dimensional analysis, you know.

David A. Smith

#3
09-22-2003, 08:00 AM
 The Ghost In The Machine Guest Posts: n/a
What's the rule about using 'ones' in algebra?

<[Only registered users see links. ]>
wrote
on Sun, 21 Sep 2003 20:33:52 GMT
<QWnbb.4796\$[Only registered users see links. ].prodigy.com> :

Depends.

In standard algebra 1 is the multiplicative identity. That is
to say, a * 1 = 1 * a = a, for all a. Also, a * 1/a = 1 for
all a != 0 (since a * 0 = 0 for all a, there's a little problem
with "1/0").

Of course a + 1 != a. But a lot of people use multiplication by
1 to solve certain problems.

For instance, how does one integrate 1 / x(x+1) ? Turns out
that one's equal to

((x+1) - x) / (x(x+1))

or (x+1) / x(x+1) - x / (x(x+1))

We can now take out the 1's (actually, a/a):

((x+1) / (x+1)) * (1 / x) - ((x / x) * (1 / (x+1)))

and we ultimately get:

1/x - 1/(x+1)

Integrating both pieces separately, we get log(x) - log(x+1) + C,
or log(x/(x+1)) + C. A bit weird-looking since log(x/(x+1))
is always negative for x > 0, but remember that log((x+1)/(x+2))
is greater than log(x/(x+1)); it's a strictly monotonic function
that asymptotically approaches the x axis. Besides, the integration
constant C can be pretty much any value one wants. :-)

I'm not sure I can think of another problem along these lines,
as it's after midnight, but you hopefully get the idea. Note
that one has to be a little careful; 1/0 has no meaning, and
0/0 can be anything at all, so it has no meaning either unless
very carefully set up using limits. For example,
lim (x->0) (x/x) = 1. However, lim(x->0) (2x/x) = 2. At x=0,
both x/x and 2x/x become 0/0.

So multiplying by 1 may introduce additional singularities over
the complex plane -- mostly because x/x has a singularity
already (namely, the point 0 + 0i).

It just takes a little care in problem setup. :-)

--
#191, [Only registered users see links. ]
It's still legal to go .sigless.
#4
09-22-2003, 12:23 PM
 Donald G. Shead Guest Posts: n/a
What's the rule about using 'ones' in algebra?

"The Ghost In The Machine" <[Only registered users see links. ]> wrote in
message news:[Only registered users see links. ]...

Thanks, _really_ Ghouly: What you say doesn't sound like a lot of
ghoulishness (pun intended) but it's beyond me. I appreciate your response.

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 thought the rule might be simple enough for me to understand; but
apparently it's not.

Thanks again Ghoully(;^)

#5
09-22-2003, 12:25 PM
 jmfbahciv@aol.com Guest Posts: n/a
What's the rule about using 'ones' in algebra?

In article <wRBbb.6129\$[Only registered users see links. ].prodigy.com>,

response.

HINT: Copy the damned lines down on paper without using slashes
to indicate divisions; instead use straight lines.

_something
to
doesn't

And has nothing to do with multiply by one.

You never really wanted an answer. Did you?

Well, perhaps a lurker benefited form the time and effort

<snip snot>

/BAH

Subtract a hundred and four for e-mail.
#6
09-22-2003, 01:54 PM
 Donald G. Shead Guest Posts: n/a
What's the rule about using 'ones' in algebra?

<[Only registered users see links. ]> wrote in message news:bkmttr\$k4\$[Only registered users see links. ].rcn.net...
Cut<
Huh? Read the question again; that wasn't it was it? It isn't all _I_ meant
anyway goofus(;^!

#7
09-22-2003, 02:08 PM
 Bill Vajk Guest Posts: n/a
What's the rule about using 'ones' in algebra?

[Only registered users see links. ] wrote:

It seems likely that Donnie is a lot brighter than folks
here realize, and that he's terribly bored.

#8
09-22-2003, 05:22 PM
 Bill Linares Guest Posts: n/a
What's the rule about using 'ones' in algebra?

First of all you have to understand that the rules of algebra are human
inventions (to quote Kroneker: "The integer numbers were created by dear
God, everything else is human-made"). The reason that "1" is a special
number is simply because it was defined that way; there is nothing mystical
about it (any Pythagoreans alive still?). The real basis for algebra are
operations (addition, subtraction, etc.); which in turn are a type of
psychological activity.

Let me see if I can give you an idea of what is all about.

-An operation is just the act of assigning two numbers within a set a third:
e.g 2+3=5. Two numbers 2 and 3 are assigned (or mapped) the 5 (Never mind
how the corresponding numbers are assigned.)

-There is this set of numbers called real numbers in which we can carry out
the two operations of addition and multiplication.

-In the addition there is a special number: the "0". Special because every
number in the set is assigned itself under addition with 0, that is: x +
0=x, for x being any number.

-In the addition we say that a number is the inverse of another if adding
them together we get the special number "0"; i.e.: x+y=0, here y is the
additive inverse of x and vice-versa.

-In the multiplication there is a special number: the "1". Special because
every number in the set is assigned itself under multiplication with 1, that
is: x * 1=x, for x being any number.

-In the multiplication we say that a number is the inverse of another if
multiplying them together we get the special number "1"; i.e.: x*y=1, here y
is the multiplicative inverse of x and vice-versa.

-In the set of real numbers, every number has an additive inverse. In the
set of real numbers every number with the exception of the 0 has also a
multiplicative inverse.

Now, when we say 1/m we mean the multiplicative inverse of m, not m itself.
It is just written in a funny way to remind us that m*1/m=1; i.e. m
multiplied times its inverse is 1, which is the way we define the inverse.

What I have outlined here is just the way mathematicians go about putting
definition upon definition, cementing it with logic to achieve this
beautiful cathedral that lots of people behold with dread: modern
mathematics. Let me just add that by taking the above definitions and some
others we arrive at what mathematicians call a field (Britannica Enc:
"Broadly speaking, a field is an algebraic system consisting of elements
that are commonly called numbers, in which the four familiar operations of
addition, subtraction, multiplication and division are universally defined
and have all their usual properties"). The whole thing is very pretty and it
is amazing that it is useful at all (but you'll have to consult Kant on
that).

#9
09-22-2003, 08:41 PM
 Bill Linares Guest Posts: n/a
What's the rule about using 'ones' in algebra?

First of all you have to understand that the rules of algebra are human
inventions (to quote Kroneker: "The integer numbers were created by dear
God, everything else is human-made"). The reason that "1" is a special
number is simply because it was defined that way; there is nothing mystical
about it (any Pythagoreans alive still?). The real basis for algebra are
operations (addition, subtraction, etc.); which in turn are a type of
psychological activity.

Let me see if I can give you an idea of what is all about.

-An operation is just the act of assigning two numbers within a set a third:
e.g 2+3=5. Two numbers 2 and 3 are assigned (or mapped) the 5 (Never mind
how the corresponding numbers are assigned.)

-There is this set of numbers called real numbers in which we can carry out
the two operations of addition and multiplication.

-In the addition there is a special number: the "0". Special because every
number in the set is assigned itself under addition with 0, that is: x +
0=x, for x being any number.

-In the addition we say that a number is the inverse of another if adding
them together we get the special number "0"; i.e.: x+y=0, here y is the
additive inverse of x and vice-versa.

-In the multiplication there is a special number: the "1". Special because
every number in the set is assigned itself under multiplication with 1, that
is: x * 1=x, for x being any number.

-In the multiplication we say that a number is the inverse of another if
multiplying them together we get the special number "1"; i.e.: x*y=1, here y
is the multiplicative inverse of x and vice-versa.

-In the set of real numbers, every number has an additive inverse. In the
set of real numbers every number with the exception of the 0 has also a
multiplicative inverse.

Now, when we say 1/m we mean the multiplicative inverse of m, not m itself.
It is just written in a funny way to remind us that m*1/m=1; i.e. m
multiplied times its inverse is 1, which is the way we define the inverse.

What I have outlined here is just the way mathematicians go about putting
definition upon definition, cementing it with logic to achieve this
beautiful cathedral that lots of people behold with dread: modern
mathematics. Let me just add that by taking the above definitions and some
others we arrive at what mathematicians call a field (Britannica Enc:
"Broadly speaking, a field is an algebraic system consisting of elements
that are commonly called numbers, in which the four familiar operations of
addition, subtraction, multiplication and division are universally defined
and have all their usual properties"). The whole thing is very pretty and it
is amazing that it is useful at all (but you'll have to consult Kant on
that).

 Tags algebra , rule

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General Science Forums     Biology Forum     New Member Introductions Forum     Chemistry Forum         Organic Chemistry Forum     Physics Forum     General Science Questions and Layperson Board         Science and Religion Forum         Zoology Forum     Environmental Sciences and Issues General Forum     Chit Chat         Science and Lab Jokes     Article Discussion     Molecular Biology News and Announcements         Conferences , Symposiums and Meetings         Molecular Station Suggestion Forum         Instructions for Posting, Help, and Frequently Asked Questions     Science News and Views         Molecular Biology Lectures and Videos     Science Careers         Post-doctoral         Medical School         Ph.D Doctor of Philosophy         Science Jobs Forum Molecular Research Topics Forum     PCR - Polymerase Chain Reaction Forum         Real-Time PCR and Quantitative PCR Forum     Bioinformatics         BioStatistics Forum     Molecular Biology Techniques         Molecular Cloning Forum         Electrophoretic Mobility Shift Assay Forum         Agarose Gel Electrophoresis Forum         BioPhysics Forum         Gene Therapy     Cell Biology and Cell Culture         Apoptosis, Autophagy, and Necrosis Forum         Flow Cytometry Forum         Transfection Forum         Confocal - Microscopy Imaging Techniques         Immunology and Host-Pathogen Interactions         Signalling Biology         Stem Cell Forum     Basic Lab Protocols and Techniques         SDS-PAGE Gel Electrophoresis Forum     DNA Techniques         DNA Extraction Forum         cDNA Forum     Epigenetics Forum: DNA Methylation, Histone and Chromatin Study         ChIP Chromatin Immunoprecipitation Forum     Protein Science         Antibody Forum             Immunoprecipitation Forum         Western Blot Forum         Protein Crystallography Forum         Recombinant Protein Forum         ELISA Assay Forum         Protein Forum     Proteomics Forum         Peptide Forum         Mass Spectrometry Forum         2-D Gel Electrophoresis Forum     Omics and Genomics Forum         Microarrays Forum         Genomics Forum     RNA Techniques Forum         RNAi and SiRNA Forum     Histology Forum         Immunohistochemistry Forum         Immunocytochemistry Forum         Electron Microscopy Forum         Immunofluorescence Forum     Protocols and Methods Forum     Molecular Biology Articles and Protocols     Animal and Molecular Model Systems         Drosophila Forum         Yeast Forum         Zebrafish Forum         Botany Forum         C Elegans Forum         Arabidopsis and Plant Biology         Microbiology Forum         Knockout Mouse Forum     Chromatography Forum Products and Vendor Discussion     Molecular Biology Products and Vendors         Bad Product/Service? Post Here         Lab Equipment Discussion and Reviews Regional Molecular Biology Discussion     Forum Chemie     Forum Biologie     Forum Biologia     Forum Chimica     Forum Physik     Forum De Chimie     Forum De Physique     Forum Chemia     中国人分子的生物学论坛 Chinese     Greek Molecular Biology Forums     分子生物学のフォーラム Japanese     ميدان فارسى. Persian Molecular Biology     [أربيك] علم ساحة- Arabic     Forum de Biologie Moleculaire     Forum Biologia Molecolare     Forum die Molekularbiologie     Foro Biologia Molecular

 Similar Threads Thread Thread Starter Forum Replies Last Post Suresh Kumar Protocols and Methods Forum 0 04-22-2009 07:40 PM shifali chatrath Protocols and Methods Forum 1 04-22-2009 08:13 AM Andreas Slateff Forum Physik 7 06-17-2005 06:21 AM Donald G. Shead Physics Forum 15 09-24-2003 08:42 AM Donald G. Shead Physics Forum 12 09-22-2003 08:25 PM

All times are GMT. The time now is 05:28 PM.

 Contact Us - Molecular Biology - Archive - Privacy Statement - Top