- #1
Someone502
- 40
- 0
i tihnk this is a dumb question but why is -x*x=-y? i tried thinking about it like a arrays on a graph but it was kinda confusing.
Why is the Product of a Negative and Positive Number Negative?
- Context: High School
- Thread starter Someone502
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Discussion Overview
The discussion revolves around understanding why the product of a negative number and a positive number is negative. Participants explore this concept through various mathematical perspectives, including axioms and properties of numbers.
Discussion Character
- Conceptual clarification
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant questions the reasoning behind the equation -x*x = -y, expressing confusion about the concept.
- Another participant explains that the product of a negative and a positive number being negative follows from mathematical axioms, providing a structured argument using the distributive property and the concept of additive inverses.
- A different participant challenges the initial equation, stating it is not universally true and emphasizes that the interpretation depends on the values of x and y.
- Clarifications are made regarding the distinction between expressions like (-x)² and -x², highlighting the importance of parentheses in determining the outcome of the operations.
Areas of Agreement / Disagreement
Participants express differing views on the interpretation of the initial equation and the reasoning behind the product of negative and positive numbers. There is no consensus on a single explanation, and multiple perspectives are presented.
Contextual Notes
Some participants reference mathematical properties and theorems without fully resolving the implications of their arguments. The discussion includes assumptions about the definitions of negative and positive numbers that are not explicitly stated.
Who May Find This Useful
This discussion may be of interest to students grappling with basic algebra concepts, educators seeking to understand common misconceptions, or anyone exploring foundational mathematical principles.
- #2
honestrosewater
Gold Member
- 2,133
- 6
You mean why the product of a negative and positive is negative? This follows from the axioms.
(-x)y + xy =[see note 1] (-x + x)y =[2] 0y =[3] 0. Since (-x)y + xy = 0,[4] (-x)y = -(xy).
1. by the distributive property
2. additive inverse
3. (0x = 0) is a theorem
4. (If x + y = 0, then x = -y) is a theorem
(-x)y + xy =[see note 1] (-x + x)y =[2] 0y =[3] 0. Since (-x)y + xy = 0,[4] (-x)y = -(xy).
1. by the distributive property
2. additive inverse
3. (0x = 0) is a theorem
4. (If x + y = 0, then x = -y) is a theorem
Last edited:
- #3
HallsofIvy
Science Advisor
Homework Helper
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"-x*x= -y"? Well, that's not always true- it depends on what x and y are!
If you mean "why is a negative number times a positive number negative?" then honestrosewater gave a pretty good answer.
(what would DIShonestrosewater smell like?)
If you are wondering about the distinction between (-x)2 and -x2, it's a matter of the parentheses: (-2)2 means (-2)(-2), a product of two negative numbers, which is positive: 4. -22 means to FIRST square: 22= 4, THEN make it negative: -4.
If you mean "why is a negative number times a positive number negative?" then honestrosewater gave a pretty good answer.
(what would DIShonestrosewater smell like?)
If you are wondering about the distinction between (-x)2 and -x2, it's a matter of the parentheses: (-2)2 means (-2)(-2), a product of two negative numbers, which is positive: 4. -22 means to FIRST square: 22= 4, THEN make it negative: -4.
Last edited by a moderator:
- #4
honestrosewater
Gold Member
- 2,133
- 6
Is there another answer?HallsofIvy said:
Fishy.
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