equalto /greater than OR greater than /equal to

Contextually I understand why it's (0,infinity) but > w/ dash under as 2 means aka till it and till it or infinity

x≤1/2 can mean (0,1/2) or (1/2,infinity)

Edited February 24Feb 24 by HbWhi5F

I understand what the formulas say, but I don't understand your question

(the infinity sign there is idiotic, but this is not your fault)

Just now, Genady said:

I understand what the formulas say, but I don't understand your question

yeah yes, I also could not see the question.

and [latex] \Delta [/latex]<0 in [latex] x^{2} -2x+3 [/latex] formula , thus it has always positive value.

Edited February 24Feb 24 by ahmet

Thread title ATOW: "≤ can mean- till it or till it OR infinity ?"

In itself there's nothing about infinity in ≤, it simply means "less than or equal to". What you call "dash under" is the result of combining < with =.

(z < 4 means z is less than 4, and won't equal 4; z ≤ 4 means z is less than or equal to 4.)

The second to last line of your image is in the form: ½ ≥right side formula > 0

i.e. with some algebra they show the right side formula must have a value from zero to half; but while it could equal half it can't equal zero.

( ½ ≥ p means half is greater than or equal to p, and also, p is less than or equal to half.)

That's used to show the left side formula (as it's equal to the right side formula) has a value in the range: (0, ½] ... where "(" is used to imply ">" that end and "]" implies "≤" that end.

Edited February 25Feb 25 by pzkpfw

6 minutes ago, pzkpfw said:

Thread title ATOW: "≤ can mean- till it or till it OR infinity ?"

In itself there's nothing about infinity in ≤, it simply means "less than or equal to". What you call "dash under" is the result of combining < with =.

(z < 4 means z is less than 4, and won't equal 4; z ≤ 4 means z is less than or equal to 4.)

The second to last line of your image is in the form: ½ ≥right side formula > 0

i.e. with some algebra they show the right side formula must have a value from zero to half; but while it could equal half it can't equal zero.

( ½ ≥ p means half is greater than or equal to p, and also, p is less than or equal to half.)

That's used to show the left side formula (as it's equal to the right side formula) has a value in the range: (0, ½] ... where "(" is used to imply ">" that end and "]" implies "≤" that end.

I've met a math teacher once who marked 5≥5 as wrong because "5 is not greater than or equal to 5 -- it is equal to 5."

1 hour ago, Genady said:

I've met a math teacher once who marked 5≥5 as wrong because "5 is not greater than or equal to 5 -- it is equal to 5."

Wow! I'd have to see the context, but that seems weird. And I'm less than or equal to the smartest person alive!

2 minutes ago, pzkpfw said:

Wow! I'd have to see the context, but that seems weird. And I'm less than or equal to the smartest person alive!

I've asked her about 6≥5. It was wrong, too, and you can guess the reasoning. ("6 is not equal to 5.")

6 hours ago, Genady said:

I've met a math teacher once who marked 5≥5 as wrong because "5 is not greater than or equal to 5 -- it is equal to 5."

I can see the argument for not using ≥ for numbers only; you need at least one to be a variable since the “or” gives an implication of having the possibility of multiple values

1 minute ago, swansont said:

I can see the argument for not using ≥ for numbers only; you need at least one to be a variable since the “or” gives an implication of having the possibility of multiple values

But this argument is wrong, at least in math:

[math](A\ge B)\Leftrightarrow (A\gt B) \vee (A=B)[/math]

[math](5=5)\Rightarrow (5=5)\vee (5>5)\Leftrightarrow (5\ge 5)[/math]

In computer architecture there are two forms of OR gates providing two different functions. They are the ""inclusive OR gate" and the "exclusive OR gate."

The inclusive OR function provides an output when both inputs are present: the exclusive OR does not provide an output when both inputs are present.

It seems to me that it is a matter of the definition of what "or" means within the context.

1 hour ago, OldTony said:

In computer architecture there are two forms of OR gates providing two different functions. They are the ""inclusive OR gate" and the "exclusive OR gate."

The inclusive OR function provides an output when both inputs are present: the exclusive OR does not provide an output when both inputs are present.

It seems to me that it is a matter of the definition of what "or" means within the context.

In mathematics, "or" is "inclusive or", and "exclusive or" is "not equivalent".