Don't you tell me one plus one equals two because one apple and one apple makes two apple.(that's what my kindergarden teacher does) When I ask you why is the sky blue you don't point me the sky and say that the sky is blue! Similarly...why makes one plus one equals to two?
2006-12-24 00:22:25 · 15 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Why is one plus one equal to two?
Why is the sky blue?
When we ask such questions we have particular definitions in mind for the words in the question.
When we ask why is the sky blue, we are asking,
why is the sky the colour that it is.
Then we are satisfied by the answer that color depends on the frequency of light that enters our eyes, and that blue corresponds to the frequency of light that reaches the earth,
from the direction of the sky,
after the atmosphere scatters the sunlight in all directions.
To answer the question , why is one plus one equal two,
we need to consider,
what do we really mean by the words "one" and "two".
Mathmeticians have sidesteped this question by
not having an independent meaning for "two",
but simply defining "two" as meaning
"one plus one".
But suppose you already have a meaning in mind for "two" that
is different than "one + one".
You would want to prove that your meaning for two is compatible with the meaning of "one plus one".
Suppose your meaning for two is based on counting.
We learn to count before we learn to add.
one, two, three, etc.
There are two ways we can think of this sequence.
The cardinal number concept, and the ordinal number concept.
The cardinal number concept is used to answer how many.
The ordinal number concept is used to answer in what order.
So, if you are thinking of the numbers one, two, three, ... etc
as first, second, third, etc,
then you really do have a profound question.
Why is the first cardinal number one
plus the first cardinal number one
equal to the second cardinal number two?
What your kindergarden teacher does still seems like the best course.
Put down two apples.
Count them.
On the first apple, you say "one"
On the second apple, you say "two".
Then we look at the same situation from a different situation.
We want to answer how many apples we have. We say the number name of the last apple counted to answer that question.
Thus,
We use the number two in two different ways at the same time.
On the one hand, it is the ordinal number of the last apple counted.
On the other hand, by natural convention, it is the cardinal number of apples that we have.
we get in the habit of using the ordinal number name as if it named how many apples we had.
We confuse the ordinal nature of the numbers with their
cardinal nature.
So,
one plus one = two because
we have used the name "two" in two different ways
interchangably.
Most of the time this confusion does not matter.
2006-12-24 12:50:45 · answer #1 · answered by kermit1941 2 · 1⤊ 1⤋
1 + 1 + 2 = 4
2016-03-29 05:30:39 · answer #2 · answered by ? 4 · 0⤊ 0⤋
There is a difference between the case of numbers and the case of the sky that you failed to point out.
Numbers (in this case, specifically counting numbers) are a man-made CONSTRUCT. The sky is not constructed by man, so we do not make up the rules for the sky.
A better analogy would be to compare counting numbers to time measures. Why are there 60 seconds in a minute? You cannot answer that question any more readily than you can answer "why is 1+1=2", since there is no inherent property or mechanism which dictates that there are 60 seconds in a minute any more than there is something specific about the concept of "1" which gives it worth beyond that granted by its creators.
In the end, we are relegated to accepting that our mathematical system works, and that our time-keeping system works, and leaving it at that.
2006-12-24 00:31:42 · answer #3 · answered by John C 4 · 2⤊ 1⤋
When man first defined our numbering system he said that if I have just a single object such as a stone in my hand, I am going to call that number "one" (in whatever language was used) and I am going to give it the symbol "1".
He then said, if I gain an additional object, then I will call tha having "two"stones and he assigned it the symbol "2".
He then saw that 1+1 was the same as two, so instead of saying I have one stone and I have one more stone, he said I have two stones. This breakthrough greatly shortened discussions when trying to tell someone how many stones you had.
In short, the answer is 1+1= 2 by definition.
2006-12-24 00:40:01 · answer #4 · answered by ironduke8159 7 · 0⤊ 1⤋
1+1 ='s it's not always 2.
If we were using a binary system of counting the answer would be 10 (only numbers are 1 and 0).
Good question, after the Math DR in the house wakes up I'll see if I can get a real answer for you. (I think John C has the correct answer)
2006-12-24 00:36:44 · answer #5 · answered by madjer21755 5 · 0⤊ 1⤋
Definitions: 1=S0, 2=S1 (i.e. 1 is the successor of 0 and 2 is the successor of 1).
Definition of +: n+0=n for all natural numbers n, n+Sm=S(n+m) for all natural numbers n and m.
Then
1+1=1+S0 (definition of 1)
=S(1+0) (definition of +)
=S1 (definition of +)
=2 (definition of 2.
2006-12-25 00:53:39 · answer #6 · answered by mathematician 7 · 1⤊ 0⤋
A is 1 letter.
B is 1 letter.
add them together you getr A B.
count the letters, 1, 2.
2006-12-24 09:57:13 · answer #7 · answered by mu_do_in 3 · 0⤊ 1⤋
Because 'two' is the arbitrary symbol given to the number you get when you put one unit with another unit.
'Blueness' is a quality that can apply to many things.
2006-12-24 00:33:32 · answer #8 · answered by langdonrjones 4 · 0⤊ 1⤋
An explanation for the Natural numbers by wikipedia:
http://en.wikipedia.org/wiki/Natural_numbers#Peano_axioms
2006-12-24 00:50:26 · answer #9 · answered by ami_malimovka 1 · 0⤊ 1⤋
Dude, its simple, self-defined logic.
If you want to be an ****** about it, then how about this: time, matter, and space all are infinitely divisible; therefore, it is actually impossible (without the implementation of faith) to prove that anything is equal even to itself.
Happy now?
2006-12-24 00:35:14 · answer #10 · answered by Anonymous · 0⤊ 1⤋