Question about properties of sums and products

In summary, the conversation discusses the validity of certain properties and the request for examples or counterexamples. The conversation also touches on the use of "if ... then" structures and basic definitions of variables in different mathematical contexts.
  • #1
MAGNIBORO
106
26
Hi and sorry for bad english.I want to know if these properties are truehttps://gyazo.com/88c471f4bb9989b67a390c372f2c72fe

and

https://gyazo.com/85f4110664db6831576012debaf3a778 I did not find these properties in any place.
so I guess it will be obvious or are incorrect,
if incorrect I would like to see counterexamples.
thanks
 
Last edited by a moderator:
Mathematics news on Phys.org
  • #2
Can you write these properties using an "if ... then" structure and not use the word "so"?

Also, can you write basic definitions of ##a##, ##b##, ##f## and so on? Are we working in the real numbers? Or a general vector space? Or?
 
  • #3
micromass said:
Can you write these properties using an "if ... then" structure and not use the word "so"?

Also, can you write basic definitions of ##a##, ##b##, ##f## and so on? Are we working in the real numbers? Or a general vector space? Or?
a and b are any whole numbers (or infinity) , f(i), g(i),t(i),b(i) are any functions of i
 
Last edited:
  • #4
For the first case, it isn't always true.
The Sum of x between 1 and 0 is 1, and the sum of x^2 between 1 and 0 is also one. We can generalise this to x^n where n is real and not equal to 0, this would produce the same answer between [0,1]
 

Related to Question about properties of sums and products

What are the properties of sums and products?

The properties of sums and products refer to the rules or characteristics that govern the addition and multiplication of numbers. These properties include commutative property, associative property, distributive property, and identity property.

What is the commutative property of addition and multiplication?

The commutative property states that the order of the numbers does not affect the result when adding or multiplying. For example, 3 + 5 = 5 + 3 and 3 x 5 = 5 x 3.

What is the associative property of addition and multiplication?

The associative property states that the grouping of the numbers does not affect the result when adding or multiplying. For example, (3 + 5) + 2 = 3 + (5 + 2) and (3 x 5) x 2 = 3 x (5 x 2).

What is the distributive property?

The distributive property states that when multiplying a number by the sum of two or more numbers, the result is the same as multiplying the number by each individual number and then adding the products. For example, 3 x (5 + 2) = (3 x 5) + (3 x 2).

What is the identity property of addition and multiplication?

The identity property states that the sum of any number and 0 is equal to the number itself, and the product of any number and 1 is equal to the number itself. For example, 5 + 0 = 5 and 5 x 1 = 5.

Similar threads

This hypothesis is right about operators on convergent and divergent series?
    • General Math
Replies
4
Views
1K
This Proof is right about sums and limits?
    • General Math
Replies
8
Views
1K
I Confused about identity for product of cosines into a sum of cosines
    • General Math
Replies
1
Views
704
I Find an explicit formula for this n-sum problem
    • General Math
Replies
7
Views
1K
I Simplify tensor product statement
    • Linear and Abstract Algebra
Replies
1
Views
890
I Partial Differential Equation solved using Products
    • General Math
Replies
2
Views
300
B Optimizing Sum of Non-Abundant Numbers
    • General Math
Replies
18
Views
2K
I The product of 2 infinite sums
    • General Math
Replies
5
Views
1K
B Can the moon orbit be used as perpetual motion?
    • Astronomy and Astrophysics
Replies
5
Views
2K
I Can chatgpt accurately calculate expected lengths in Pascal's triangle?
    • General Math
2
Replies
66
Views
4K

Hot Threads

Recent Insights

Back
Top