this is an example of what i am talking about:
0----------1----------2---------3 these lines represent 1+1=2
by looking at numbers represented by lines it appears that 1+1 actually ends past 2 and at three. I know that 1+1=2 when we think of numbers as being a whole like two apples, but in reality when the second apple is added havent we completed two and reached three? I guess you could even contend that the apple is at its greatest amount in the middle and recedes as the apple is "completed".
Basically what I am asking is how is the beginning or end of a number decided on. The line i made and connected is something i just decided on but could obviously be different if someone else drew the lines of any length.
Am I making any sense or does this sound REALLY dumb?
Someone gives you another dollar.
You now have 2 dollars.
Although the idea have haveing an infinite amount of money when someone gives you a buck is nice, it doesn't really work.
BTW they are not lines, they are segments and segments do not continue on...
well, thanks i had a feeling id get creamed for that question.
but where on you dollar did it equal one? at one edge or do you have to move across to the opposite edge? and, going left to right, if the left edge is the start of one doesn't the right edge mean that one is over? and what is in between one and two, by your reasoning one and two dollars are separate. is there a grand canyon between one and two?
okay so im dumb!
2. The number line when used with integers is just a device to demonstrate
some of the properties of numbers, it is in no way a definition of them.
The definition of intergers is usualy based on the idea of collections of
discrete objects (like apples), and placing these collections into one-to-one
relations with other collections.
3. Think of it this way if I am selling apples at $1 each and you bring me two
apples would you be happy if I charged you $3?
two. If you were talking about other kinds of numbers no there is not a gap
between 1 and 2 it is filled with fractions, or the real numbers depending
on what system we are working in.
But integers are used to enumerate discrete objects, and they only come
in discrete lumps and are not considered divisible as far as the integers are
(remember in maths if you are finding a concept difficult to understand then
you are thinking about it in the wrong way - find a better way and it will
it is our job to try to help them. Your post does not do that, and its net result
may be that lime goes away with a worse impressions of maths and maths-heads
than they had before.
Now it may turn out that lime is a troll, but you have to give them the
chance to prove that, not just assume it.
In many cases where a question is confused it is correct to ask for
clarification because it is obvious that the poster has a question that they
are summarising incompletely or confusingly, but not here it is the poster
who is confused and needs help.
In this case it would be better if you had nothing constructive to say that
you had remained silent.
There are no dumb question