Question

logic:

x - 1 >= 0
x > 0

i dont understand when i can remove the equal sign, can somebody explain it to me?

Answer 1

and what about

\[x+1\ge0\]

for example

Answer 2

those are two different statements

what is the difference between\[x\ge0\]and\[x>0\]is basically your question?

Answer 3

or what about
\[x+1\le0\] or \[x-1\le0\]

Answer 4

one question at a time please jessica, you are asking different kinds of questions

Answer 5

i understand what the sign means.. but like my example..

we gonna take this on:

x -1 >= 0

this is the same as: x > 0

Answer 6

but how?

Answer 7

no it is not
take it one step at a time
what do\[x>0,x\ge0,x<0\x\le0\]all mean

Answer 8

\[x-1\ge0\implies x\ge1\]which is not the same as \[x>0\]what gives you this impression?

Answer 9

i mean, what makes you think they are the same?

Answer 10

look better the equal sign is now gone..

Answer 11

ok so let me get this straight:
your question is
"how is \(x-1\ge0\) the same as \(x>0\) ?"
that answer is: it's not.

Answer 12

never mind then, this is what my teacher said

Answer 13

look, they are not the same, but one \(implies\) the other

Answer 14

if \(x-1\ge0\) then \(x\ge1\)
from thinking about the number line, it is obvious that if a number is \(\text{at least 1}\) then is must always be greater than zero, so we can write\[x\ge1\implies x>0\]the arrow is read as the word "implies"
the statement above is
" since x is at least 1, that implies that x is more than zero"
which makes sense, right?

Answer 15

it does make sense, but im still confused a little bit

Answer 16

we cannot write\[x\ge1\implies x\ge0\] because that is like saying
"since x is at least 1, that implies that x is at least 0"
but \(at\) \(least\) implies x it cannot be less than 1, so x=0 is not possible

Answer 17

... a contradiction^

the fact that\[x\ge1\implies x>0\]is trivial
"if the number is at least 1 it's more than zero"
is a trivial statement
we could just as easily have written\[x\ge1\implies x>\frac12\implies x>\frac14\implies x>-420,\text{etc.} \]because \[x\ge0\] implies that x is bigger than all those numbers I wrote above

Answer 18

you could read the above line that is second tp last as
"if x is at least 1, then it's more than 1/2, and 1/4, and -420"
of course we could write any number less than one in those places

Answer 19

oehh... i still find it difficult :S

Answer 20

new ideas are always a little strange, but I promise you that if you meditate on it for a while it will seem kinda obvious
I often think of
\(\ge\) which is "greater-than or equal-to" as the phrase "at least"
and
\(\le\) which is "less-than or equal-to" as "at most
so\[0\le x\le1\]means
"x is at least 0 and at most 1"

drawing number lines also helps in these situations too

Answer 21

you tell me, what is the difference between\[x\ge0\]and\[x>0\]

Answer 22

x>=0 is: 0,1,2,3,4....
x>0 is: 1,2,3,4....

Answer 23

why are you using only integers?
x>0 is 1/2, 3/10 as well
but yeah, the equals sign means that number is \(included\) in the interval of x we are talking about
without the equals sign the number itself is not included

Answer 24

it is like the difference between the phrases
"at least"
and
"more than"

Answer 25

its just an habbit, i always use discreet :P

Answer 26

\[x\ge0\]x is at least zero\[x>-5\]x is more than -5

-notice those statements do not contradict
also notice that -5 could have been any number less than 0