# algebraic expressions

Printable View

• September 3rd 2009, 05:30 PM
pklanni
algebraic expressions
I am a dad helping with daughters homework and have a symbol I have not seen, the symbol is a solid diamond. The problem reads
Quote:

A new operation is defined as a ( solid diamond ) b = a+a-b. Is the set of whole numbers closed under the operation ( solid diamond )? If not, give a set that is closed under this operation.
Can anyone tell me what I am supposed to do with the solid diamond? Thank you in advance.
• September 3rd 2009, 05:49 PM
artvandalay11
a (diamond) b=a+a-b

5 (diamond) 2=5+5-2=8

The set of whole numbers is not going to be closed under this new operation (which is simply a combination of familiar operations in addition and subtraction) because the set of whole numbers is not closed under addition and subtraction

Here I am assuming the set of whole numbers is {0,1,2,3,.....}

however the set of integers and real numbers will be closed. The set of whole numbers are not closed because if b is large enough, a+a-b could be negative, and thus the result would not be an element of the whole numbers
• September 3rd 2009, 05:52 PM
pickslides
You are given $a\diamond b = a+a-b$

So now think, if a = 2 and b = 3 now

$2\diamond 3 = 2+2-3 = 1$

The diamond symbol is not an operation in particular, just defined for this particualr problem.

Even easier

$a\diamond b = a+a-b = 2a-b$
All times are GMT -8. The time now is 04:00 PM.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.938949465751648, "perplexity_flag": "middle"}