anonymous
  • anonymous
logic: x - 1 >= 0 x > 0 i dont understand when i can remove the equal sign, can somebody explain it to me?
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
and what about \[x+1\ge0\] for example
TuringTest
  • TuringTest
those are two different statements what is the difference between\[x\ge0\]and\[x>0\]is basically your question?
anonymous
  • anonymous
or what about \[x+1\le0\] or \[x-1\le0\]

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TuringTest
  • TuringTest
one question at a time please jessica, you are asking different kinds of questions
anonymous
  • anonymous
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
anonymous
  • anonymous
but how?
TuringTest
  • TuringTest
no it is not take it one step at a time what do\[x>0,x\ge0,x<0\x\le0\]all mean
TuringTest
  • TuringTest
\[x-1\ge0\implies x\ge1\]which is not the same as \[x>0\]what gives you this impression?
TuringTest
  • TuringTest
i mean, what makes you think they are the same?
anonymous
  • anonymous
look better the equal sign is now gone..
TuringTest
  • TuringTest
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.
anonymous
  • anonymous
never mind then, this is what my teacher said
TuringTest
  • TuringTest
look, they are not the same, but one \(implies\) the other
TuringTest
  • TuringTest
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?
anonymous
  • anonymous
it does make sense, but im still confused a little bit
TuringTest
  • TuringTest
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
TuringTest
  • TuringTest
... 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
TuringTest
  • TuringTest
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
anonymous
  • anonymous
oehh... i still find it difficult :S
TuringTest
  • TuringTest
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
TuringTest
  • TuringTest
you tell me, what is the difference between\[x\ge0\]and\[x>0\]
anonymous
  • anonymous
x>=0 is: 0,1,2,3,4.... x>0 is: 1,2,3,4....
TuringTest
  • TuringTest
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
TuringTest
  • TuringTest
it is like the difference between the phrases "at least" and "more than"
anonymous
  • anonymous
its just an habbit, i always use discreet :P
TuringTest
  • TuringTest
\[x\ge0\]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

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