You mentioned that "technically you do not write an equal sign next to an English word." and that you are "replacing the entire sentence with mathematical symbols," but when you write "1/0 is undefined" you are writing the mathematical symbols "1/0" next to the English word "is."
@MegaDarthraider: I said you do not write an equal sign (=) next to a regular word. You use an equal sign when there is a mathematical expression on each side of the equal sign. But I didn't say you had to write words only next to the word "is". It is perfectly okay to write "is" next to mathematical symbols. "He is 16", for instance, is a perfectly fine English sentence. Also, I meant in that example, I replaced the entire sentence with mathematical symbols. I hope that is more clear. : )
What kind of "lollipop" is 0/0? :-) and why is it not proper to write "= undefined" @ 09:49 you say "you don't want to write the word equals because it doesn't actually equal anything we say it IS undefined because we can't even define it to be any number at all"... but generally speaking "=" means "is."
@MegaDarthraider: If 0 is in the denominator, the expression is undefined. So 0/0 is a yucky lollipop sticking to floor, and is undefined. The equal sign (=) is for algebraic or numerical expressions, so technically you do not write an equal sign next to an English word. You can translate English sentences with the word is to words, like "Two more than a number is six" can be written n+2=6. I'm replacing the entire sentence with mathematical symbols, NOT writing: Two more than a number=six
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Please have a look at this online file:
dynamic.uoregon.edu/~teddy/OnDivisionByZero.pdf
MegaDarthraider 8 months ago
@videosbyjulieharland: Thank you for your reply.
You mentioned that "technically you do not write an equal sign next to an English word." and that you are "replacing the entire sentence with mathematical symbols," but when you write "1/0 is undefined" you are writing the mathematical symbols "1/0" next to the English word "is."
MegaDarthraider 8 months ago
@MegaDarthraider: I said you do not write an equal sign (=) next to a regular word. You use an equal sign when there is a mathematical expression on each side of the equal sign. But I didn't say you had to write words only next to the word "is". It is perfectly okay to write "is" next to mathematical symbols. "He is 16", for instance, is a perfectly fine English sentence. Also, I meant in that example, I replaced the entire sentence with mathematical symbols. I hope that is more clear. : )
videosbyjulieharland 8 months ago
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MegaDarthraider 8 months ago
What kind of "lollipop" is 0/0? :-) and why is it not proper to write "= undefined" @ 09:49 you say "you don't want to write the word equals because it doesn't actually equal anything we say it IS undefined because we can't even define it to be any number at all"... but generally speaking "=" means "is."
MegaDarthraider 8 months ago
@MegaDarthraider: If 0 is in the denominator, the expression is undefined. So 0/0 is a yucky lollipop sticking to floor, and is undefined. The equal sign (=) is for algebraic or numerical expressions, so technically you do not write an equal sign next to an English word. You can translate English sentences with the word is to words, like "Two more than a number is six" can be written n+2=6. I'm replacing the entire sentence with mathematical symbols, NOT writing: Two more than a number=six
videosbyjulieharland 8 months ago
To see why a quotient like a/0 is undefined in the set of real numbers is to note that division is defined by multiplication
which becomes an identity in the case of the denominator equaling zero:
a/b = c is defined by a = b*c Let b = 0. If a/0 = c, then a = 0*c But 0*c = 0. <--identity!
Hence, if a =/= 0 no value of c can make the statment a = 0*c true, while if a = 0, every value of c will make the statement true.
Thus, a/0 either has no value or is indefinite in value.
MegaDarthraider 9 months ago