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Hi everybody.
Please, I wonder how to read the following mathematical expressions aloud in English:
{a,b,c} ∅ a∈S a∉S A ⊂ B a < b a≥b P ⇒ Q P ⇔ Q (∃ x) (∀ x) lim 1/x²=+oo (=(la limite de 1 sur x à la puissance 2 lorsque x tend vers 0 à droite est égal à plus l'infini) x>0
Thank you so very much.


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Khalid Sami wrote:Hi everybody.
Please, I wonder how to read the following mathematical expressions aloud in English:
some of these depends on context. My maths is geophysics orientated, so I might not be using the same meaning you are, but
{a,b,c} set with elements a b c ∅ an empty set a∈S a is an element of set S a∉S a is not an element of set S A ⊂ B A is a subset of B (strict subset with fewer elements) a < b a is less than b a≥b a is greater than or equal to b P ⇒ Q P implies Q P ⇔ Q P is equivalent to Q (∃ x) there exists x (∀ x) for all x lim 1/x²=oo(=infini) not entirely sure what your expression is, but the general wording I would use for those symbols in that order would be limit of one over x squared equals infinity, but for the function, it would be limit of one over x squared as x goes to infinity x>0 not sure, don't recognise that, unless it is an expression x minus a number greater than zero.
Thank you so very much.


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thar wrote: lim 1/x²=oo(=infini) not entirely sure what your expression is, but the general wording I would use for those symbols in that order would be limit of one over x squared equals infinity, but for the function, it would be limit of one over x squared as x goes to infinity x>0 not sure, don't recognise that, unless it is an expression x minus a number greater than zero.
Wow, thar, I can think of quite a few native speakers of English who would have had a difficult time trying to puzzle that out. ∅ is also sometimes referred to as "the null set" or just "null". I think these last two haven't been properly typed due to the limitations of text layout in HTML. lim x → ∞ 1/x² = y When properly typeset, the expression " x → ∞" would appear under the symbol "lim" and be read as "as x approaches infinity," or "as x goes to infinity." The part in green is optional and the variable or value would differ depending on context. Similarly, the last example looks like it should be "x → 0" which would be spelled out "as x approaches zero". In some programming languages this might be interpreted as "decrement x by 1 for each iteration through the loop while x is greater than zero".


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Looks good to me... I don't remember much about this stuff. The function *y = 1/x^2 or f(x) = 1/x^2 is a hyperbola (below).
To correctly "read" aloud the entire limit : * y equals one over x squaredThe limit of y = 1/x^2 as x approaches zero from the right is equal to positive infinity. The limit of y = 1/X^2 as x approaches zero from the left is equal to positive infinity.
Therefore the limit of y = 1/x^2 as x approaches zero is equal to positive infinity.
Graph: y = 1/x^2 http://blog.flyingcoloursmaths.co.uk/wpcontent/uploads/2012/01/recipsq.png


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RubyMoon wrote:Looks good to me... I don't remember much about this stuff. The function y = 1/x^2 or f(x) = 1/x^2 is a hyperbola (below).
To correctly "read" aloud the entire limit : The limit of y = 1/x^2 as x approaches zero from the right is equal to positive infinity. The limit of y = 1/X^2 as x approaches zero from the left is equal to positive infinity.
Therefore the limit of y = 1/x^2 as x approaches zero is equal to positive infinity.
Graph: y = 1/x^2 http://blog.flyingcoloursmaths.co.uk/wpcontent/uploads/2012/01/recipsq.png You could be right. I didn't think of the possibility that infinity is the solution, not the limit of x.


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Thank you so very much. This is the correct expression for the last one: lim 1/x²=+∞. x→0+


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leon  No, it isn't the limit of x.
You are taking the limit of the function... meaning what "happens" to the value for y as x approaches zero  as you plug in values for x as you "approach" or get closer to the origin (0, 0).
As x takes on the values 3, 2, 1, etc. (from the left), the value of the function (y) increases positively as the graph shows the line crawling "up" the yaxis and getting infinitely closer and closer.... forever. Same deal as x approaches zero from the right.


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Khalid Sami wrote:Thank you so very much. This is the correct expression for the last one: lim 1/x²=+∞. x→0+ Oops, I totally misunderstood that as two separate expressions. Sorry for the noise. Edited to add: Even worse, the correct interpretation was right there in French all along.


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[quote=Khalid Sami]Thank you so very much. This is the correct expression for the last one: lim 1/x²=+∞. x→0+
Yes, that's correct. I'd put the + sign in front of the 0.
(and if I were writing it out the + sign would be small  to the upper left of the zero.)


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From a rigorous point of view, unfortunately this is not a good example, since when x tends to zero (in symbols: x > 0) the expression 1/x² diverges. Or, one may also say that the function f(x) = 1/x² has no limit when x > 0. If one wants to include infinity into the formalism, one needs to to work in the extended complex plane (or Riemann sphere).
To become familiar with the English terms, a better example would be lim 1/x² = 0 as x > ∞ , in words: The limit of one over x squared equals zero when x tends to infinity (where the latter means that for any given natural number n one may take a x greater than n, x > n).


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Thanks Jean.
(I was restricting my answer to the OP's original question and continuing on with thar's post.)
lim 1/x²=+oo (=(la limite de 1 sur x à la puissance 2 lorsque x tend vers 0 à droite est égal à plus l'infini) x>0
Since that particular limit (above) goes to +infinity I was going to call it "undefined" or say "the limit does not exist".... couldn't remember.
Hope you're not confused, Khalid !


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Please, is the following correct too?: a∈S = a belongs to S. A ⊂ B= A is included in B.


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Yes  and I'd go with thar's answers:
a∈S a is an element of set S (belongs to...) a∉S a is not an element of set S A ⊂ B A is a subset of B (strict subset with fewer elements) (included in...)
Also the Wolfram site is very helpful.
Sorry this got confusing  it can be written as you have done so here:
lim 1/x²=+∞. x→0+


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Million Thanks to all of you: thar, leon, Ruby, jyrka and jean. I'm so happy for your good help.


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