One multiplied by one is two. One instance of one is one. One times one is one.
The square root of two is one.
In a proper real world counting system, a proper ruler would consist of inch increments whereby each subsequent inch, was longer than the one before it, and if you knew the proper amount to increase each increment, your math could always result in rational numbers.
I have 4 chickens, and each chicken lays 4 eggs.
Thats 16 eggs.
I walk into the barn and I see 16 eggs and I say, how many chickens laid 4 eggs, and I say 4.
If I say, I want to optimize chicken capacity, and find out how many equal chicken egg units, I need to arrive at 16 eggs, then I can square that amount and end up with 4 chickens 4 eggs.
I walk into the barn, there are two chickens and two eggs. Both are walking funny.
Is it not, prudent, for me to assume, that one chicken did not lay 1.4 to infinity eggs 1.4 to infinity times?
Is it not more rational then to assume that each chicken laid one egg?
If I say, that mysteriously 2 apples appeared on the teachers desk two times out of thin air and then disappeared into thin air, and they were the same apples each time, because I saw they had numbered stickers on them, so two instances of two apples appeared on the teachers desk. How many apples were there?
2 apples.
If I say, mysteriously apples began to multiply on the teachers desk, as twice 2 apples appeared out of thin air.
4 apples. I am using the term multiplied, and the term twice.
Rephrased two apples mysteriously appeared two times on the teachers desk. 2 apples.
The apples multiplied as two times two apples appeared on the teachers desk.
So then the reason the square root of two is one, is that the function of multiplying real objects, means to increase their number. Whereas 'instances of', which is easily confused with 'multiplied by' refers to events where the number of actual apples is ambiguous, And when you talk about square root, the opposite of square root is multiply, not instance of.
Therefore, one times one, equals one instance of one, and is not the same as one multiplied one time, as one multiplied one time, means that the number of apples increased once, which means that one times one equals two.
If we use Pythagorean Theorem, to prove the square root of 2 we are not dealing in real world objects, we are now dealing in imaginary lines and ambiguous smeared out infinitely divisible imaginary quantities. However, Farmer Brown's conjecture states, that given the proper ruler, with the proper incremented counting system, your result would be a rational finite number.
Jon Slaughter wrote: > If 8 ducks equals 24.384 chickens then Farmer Brown concludes that he lost > 3.1434 ears of corn.
> Properly incrementing his i59 geese Farmer Brown prudently finds a rational > apple.
> Therefor surely the apples multiply faster than the corn?
> Is it not true that the barn holds e^pi^e eggs?
> -----
> Me thinks farmer brown needs to stop counting on his fingers and use a > calculator.
You city slickers wouldn't know a hen from a rooster.
To prove Farmer Brown's first conjecture, that one multiplied one time, equals two, I will have to use a city slicker analogy.
Mr. Barnum, is in his lab, and he looks in his microscope and he proclaims... "Oh, My, God, they are multiplying!" "I was looking at this cell, and it multiplied, one time, and now there are two cells"
ipso facto and hence, one multiplied one time equals two.
Mr. Barnum, looks again at a different slide and he says, "Hmmm... there are two cells, two identical cells, that is a sum, and this sum I will call the square, and now then, if this is my sum I am calling the square, what is the root of that square? What is the root cause of that square? Cell division. One cell, divided, into two cells. By this cell division, one has multiplied into two! Therefore, the root of two is one"
Rick wrote: > Jon Slaughter wrote: >> If 8 ducks equals 24.384 chickens then Farmer Brown concludes that he >> lost 3.1434 ears of corn.
>> Properly incrementing his i59 geese Farmer Brown prudently finds a >> rational apple.
>> Therefor surely the apples multiply faster than the corn?
>> Is it not true that the barn holds e^pi^e eggs?
>> -----
>> Me thinks farmer brown needs to stop counting on his fingers and use a >> calculator.
> You city slickers wouldn't know a hen from a rooster.
> To prove Farmer Brown's first conjecture, that one multiplied one time, > equals two, I will have to use a city slicker analogy.
> Mr. Barnum, is in his lab, and he looks in his microscope and he > proclaims... > "Oh, My, God, they are multiplying!" > "I was looking at this cell, and it multiplied, one time, and now there > are two cells"
> ipso facto and hence, one multiplied one time equals two.
> Mr. Barnum, looks again at a different slide and he says, "Hmmm... there > are two cells, two identical cells, that is a sum, and this sum I will > call the square, and now then, if this is my sum I am calling the > square, what is the root of that square? What is the root cause of that > square? Cell division. One cell, divided, into two cells. By this cell > division, one has multiplied into two! Therefore, the root of two is one"
So then, I have proven that through cell division, one multiplied one time equals two.
Where is your mathematical proof, which you are basing your calculations, and calculators on, that one multiplied one time equals one? Or this merely a papal declaration?
> One multiplied by one is two. > One instance of one is one. > One times one is one.
> The square root of two is one.
If the square root of two were one, the square root of four would also be one, by your reasoning. After all, one instance of four is one--right? One times four is one. One instance of four cannot be four instances; otherwise, 1=4.
To a mathematician, it very much matters what one means by "one" and "two." These are not "instances;" they are values. If one cannot differentiate one value from another, arithmetic does not exist.
The technical term you are missing, is "multiplicative identity." It means that the integer 1 does not change the identity of any other value by which it is multiplied. Similarly, the number zero is called "additive identity" in that it does not change the identity of any value to which it is added.
Getting to square roots--we derive the value square root of two by adding one side of the square to one side of the square. There are two "instances" of one, not one. The hypotenuse is therefore one "instance" of two. The multiplicative identity holds.
That the square root of two is irrational pertains to its relation to the sides of the right triangle of which the hypotenuse is a member. Complete the square on the other side of the hypotenuse, and you have your rational increase, counting the sides. As easy as 2+2=4. No need to make new rulers.
> In a proper real world counting system, a proper > ruler would consist > of inch increments whereby each subsequent inch, was > longer than the > one before it, and if you knew the proper amount to > increase each > increment, your math could always result in rational > numbers.
> I have 4 chickens, and each chicken lays 4 eggs.
> Thats 16 eggs.
> I walk into the barn and I see 16 eggs and I say, how > many chickens > laid > 4 eggs, and I say 4.
> If I say, I want to optimize chicken capacity, and > find out how many > equal chicken egg units, I need to arrive at 16 eggs, > then I can > square > that amount and end up with 4 chickens 4 eggs.
> I walk into the barn, there are two chickens and two > eggs. > Both are walking funny.
> Is it not, prudent, for me to assume, that one > chicken did not lay 1.4 > to infinity eggs 1.4 to infinity times?
> Is it not more rational then to assume that each > chicken laid one > egg?
> If I say, that mysteriously 2 apples appeared on the > teachers desk two > times out of thin air and then disappeared into thin > air, and they > were the same apples each time, because I saw they > had numbered > stickers on them, so two instances of two apples > appeared on the > teachers desk. > How many apples were there?
> 2 apples.
> If I say, mysteriously apples began to multiply on > the teachers desk, > as twice 2 apples appeared out of thin air.
> 4 apples. I am using the term multiplied, and the > term twice.
> Rephrased two apples mysteriously appeared two times > on the teachers > desk. > 2 apples.
> The apples multiplied as two times two apples > appeared on the teachers > desk.
> So then the reason the square root of two is one, is > that the function > of multiplying real objects, means to increase their > number. Whereas > 'instances of', which is easily confused with > 'multiplied by' refers > to events where the number of actual apples is > ambiguous, > And when you talk about square root, the opposite of > square root is > multiply, not instance of.
> Therefore, one times one, equals one instance of one, > and is not the > same as one multiplied one time, as one multiplied > one time, means > that the number of apples increased once, which means > that one times > one equals two.
> If we use Pythagorean Theorem, to prove the square > root of 2 we are > not dealing in real world objects, we are now dealing > in imaginary > lines and ambiguous smeared out infinitely divisible > imaginary > quantities. > However, Farmer Brown's conjecture states, that given > the proper > ruler, with the proper incremented counting system, > your result would > be a rational finite number.
On Oct 7, 10:32 am, "T.H. Ray" <thray...@aol.com> wrote:
> > One multiplied by one is two. > > One instance of one is one. > > One times one is one.
> > The square root of two is one.
> If the square root of two were one, the square root > of four would also be one, by your reasoning. After > all, one instance of four is one--right? One times four > is one. One instance of four cannot be four instances; > otherwise, 1=4.
No you are mistaken. I am saying multiplied by, not instance of.
Mr. Barnum peered with awe into his microscope and proclaimed "They are multiplying!" "The cells! They are multiplying by cell division. One cell multiplied one time into two cells I saw it with my own eyes"
One cell multiplied into two cells, the cells went forth and multiplied.
Once multiplied into two, and the reverse, one cell divided into two, and since one cell multiplied into two, one multiplied one time equals two, hence the square root of two is one.
That is my proof and I would love to see your proof, that one multiplied one time equals one.
> On Oct 7, 10:32 am, "T.H. Ray" <thray...@aol.com> > wrote: > > > One multiplied by one is two. > > > One instance of one is one. > > > One times one is one.
> > > The square root of two is one.
> > If the square root of two were one, the square root > > of four would also be one, by your reasoning. > After > > all, one instance of four is one--right? One times > four > > is one. One instance of four cannot be four > instances; > > otherwise, 1=4.
> No you are mistaken. I am saying multiplied by, not > instance of.
That's not what you said. As long as I am laid up in bed today, though, we might as well indulge in a little silliness.
> Mr. Barnum peered with awe into his microscope and > proclaimed "They > are multiplying!" > "The cells! They are multiplying by cell division. > One cell multiplied > one time into two cells I saw it with my own eyes"
Mr. Barnum saw one cell divide into two, not multiply. Or don't you accept that 1+1=2?
> One cell multiplied into two cells, the cells went > forth and > multiplied.
> Once multiplied into two, and the reverse, one cell > divided into two, > and since one cell multiplied into two, one > multiplied one time equals > two, hence the square root of two is one.
Division is certainly the inverse (not reverse) of multiplication; however, division of any integer, => 1, by itself is one. Did you not get my point about multiplicative identity? Look it up.
> That is my proof and I would love to see your proof, > that one > multiplied one time equals one.
> > On Oct 7, 10:32 am, "T.H. Ray" <thray...@aol.com> > > wrote: > > > > One multiplied by one is two. > > > > One instance of one is one. > > > > One times one is one.
> > > > The square root of two is one.
> > > If the square root of two were one, the square root > > > of four would also be one, by your reasoning. > > After > > > all, one instance of four is one--right? One times > > four > > > is one. One instance of four cannot be four > > instances; > > > otherwise, 1=4.
> > No you are mistaken. I am saying multiplied by, not > > instance of.
> That's not what you said. As long as I am laid up in > bed today, though, we might as well indulge in a little > silliness.
> > Mr. Barnum peered with awe into his microscope and > > proclaimed "They > > are multiplying!" > > "The cells! They are multiplying by cell division. > > One cell multiplied > > one time into two cells I saw it with my own eyes"
> Mr. Barnum saw one cell divide into two, not multiply. > Or don't you accept that 1+1=2?
Division is the opposite of multiplication and by good fortune, both were observed. The cells multiplied by dividing and that is what you would expect given the uniqueness of the number one.
> > One cell multiplied into two cells, the cells went > > forth and > > multiplied.
> > Once multiplied into two, and the reverse, one cell > > divided into two, > > and since one cell multiplied into two, one > > multiplied one time equals > > two, hence the square root of two is one.
> Division is certainly the inverse (not reverse) of > multiplication; however, division of any integer, > => 1, by itself is one. Did you not get my point about > multiplicative identity? Look it up.
One cannot be a prime number.
> > That is my proof and I would love to see your proof, > > that one > > multiplied one time equals one.
