How about ##e^2## times ##\pi##? What's the repeated addition that produces this product?Randy Beikmann said:Your statements don't address my comments. I agreed from the start that, if using pure numbers, multiplication can be seen as repeated addition.
I mean what a calculator does is approximate an value for these numbers then you get a pure number plus fraction. Or I can think of it as there is an answer to this if you get more and more closer to the values until the rest becomes negligible.Mark44 said:How about ##e^2## times ##\pi##? What's the repeated addition that produces this product?
If you approximate ##e^2## as 7 and ##\pi## as 3, you can certainly write 7 * 3 as 7 + 7 + 7, or 21. It gets harder if you approximate the two numbers as 7.4 and 3.1. How do you add 7.4 to itself 3.1 times? You can't express the product 7.4 * 3.1 purely as an addition.Biker said:I mean what a calculator does is approximate an value for these numbers then you get a pure number plus fraction. Or I can think of it as there is an answer to this if you get more and more closer to the values until the rest becomes negligible.
I don't get why you can't divide or I can just look at it like this: add 7.4 three times and then find out what is 1/10 of 7.4.. 0.74 If I add this 10 times it gives me 7.4Mark44 said:If you approximate ##e^2## as 7 and ##\pi## as 3, you can certainly write 7 * 3 as 7 + 7 + 7, or 21. It gets harder if you approximate the two numbers as 7.4 and 3.1. How do you add 7.4 to itself 3.1 times? You can't express the product 7.4 * 3.1 purely as an addition.
You might say, well, we can look at 74 * 31, and then add calculate 74 + 74 + 74 + ... + 74, where there are 31 terms being added. However, the answer will by too large by a factor of 100, so you're then going to have to divide the answer by 100. So even with this trick, we're still not able to do 7.4 times 3.1 purely as an addition problem.
You can only divide if you have defined what division means. Division is normally defined in terms of multiplication. We are still working on getting you to tell us how you define multiplication for decimal fractions.Biker said:I don't get why you can't divide or I can just look at it like this: add 7.4 three times and then find out what is 1/10 of 7.4.. 0.74 If I add this 10 times it gives me 7.4
And what do you do about the non-computable real numbers?Biker said:I mean what a calculator does is approximate an value for these numbers then you get a pure number plus fraction. Or I can think of it as there is an answer to this if you get more and more closer to the values until the rest becomes negligible.
But the claim is that multiplication is repeated addition, and only addition.Biker said:I don't get why you can't divide or I can just look at it like this: add 7.4 three times and then find out what is 1/10 of 7.4.. 0.74 If I add this 10 times it gives me 7.4
Baluncore said:If I make an equilateral-triangle into a right-angle-triangle by stretching one side to make its length √2, how can I lengthen that side by repeated addition ?
Well you are making a distinction between numbers and the things that they are numbers of.Randy Beikmann said:Your statements don't address my comments. I agreed from the start that, if using pure numbers, multiplication can be seen as repeated addition. The issue I have is when applying the mathematics, and the numbers are accompanied by units. Baluncore gave another similar example above.
rootone said:Is Zero considered to a member of the set of natural numbers by advanced students of math?
Intuitively it strikes me that the absence of a thing is not included in idea of 'a quantity of things'.
For example you cannot accuse somebody of stealing zero amount of cash.
OK, but that means negative numbers also are in the set of natural numbers.AgentCachat said:You can "accuse" a check writer of having zero amount of cash if they in fact have no money in the bank.
What if a can be derived from b, which can be derived from c, and c can be derived from a. What is fundamental there?_PJ_ said:Surely if something is derived (or can be derived) from another, then this rules out that something as a fundament and may enforce the 'fundamentality' of the other.
My guess would be that a,b, and c are the same thing and the distinction depends on the state (or choice maybe?),of the observer.Baluncore said:What if a can be derived from b, which can be derived from c, and c can be derived from a. What is fundamental there?
No. I must disagree; there is one definition of fundamental.Baluncore said:What if a can be derived from b, which can be derived from c, and c can be derived from a. What is fundamental there?
Unfortunately, there can be many definitions of the term “fundamental”.
If that's your definition of fundamental, then addition of natural numbers is not fundamental. We define addition as ##a+S(b) = S(a+b)## where ##S## is the successor operator._PJ_ said:Surely if something is derived (or can be derived) from another, then this rules out that something as a fundament and may enforce the 'fundamentality' of the other.
¿?
who's "we" and why is the current mode of pregerred definition assumed to have any real objective arbitration over the nature of fundament?pwsnafu said:If that's your definition of fundamental, then addition of natural numbers is not fundamental. We define addition as ##a+S(b) = S(a+b)## where ##S## is the successor operator.
I agree that there can be only one definition in anyone field. But here we are discussing multiple different fields. Mathematics requires internal consistency, while a post-modernist analysis allows for many interpretations in many different fields, or schools of thought. For example; teaching arithmetic to children, or the assumptions that underly formal mathematics._PJ_ said:No. I must disagree; there is one definition of fundamental.