Quote: A Horseradish @ 23rd April 2015, 1:28 PM BSTThat does look right, yes, and it is neat. To have it as 6< would be "what is 6 less than?" which means the same thing as "what is more than 6?" but 6< probably looks better in a construction.
In the first case there, 6 is less than x so x is definitely 7. In the second, so far as it makes sense, any number that goes before <6 must be less than 6. So the main point surely is how you define and indeed describe "less than" symbolically depends on what "less than" is being used in relation to.
I think you have a concept here that if you stick an x or a number against 6> or 6<, it then relates to something - which is correct : it relates to whatever it is stuck against, eg 6<x, 6<7 - but that if you don't do that at that start and just say "less than 6", ie >6, it doesn't relate to anything much at all.
It's standing alone in that thinking. In mid air. As if it is some sort of entity of itself.
But it does relate to something. In actuality, it relates to all the numbers lower than 6.
The reason why you are not grasping that fully is that without the x or a number preceding it - and being in the form of a question which someone else has to answer - it appears to you that what it relates to at the start is so invisible that the phrase "less than six" or >6 is absent of full context.
Look at this way.
I say "bat and ball" or "ball and bat"? What is the better phrase? You say it's "bat and ball". Fine. So then I say but is it "bat and?" or "ball and?"? You reply it depends on the context. If the answer is "ball", it's "bat and?" If it's "chain", it's "ball and". And I say "oh no, I'm asking how the question must be asked. It's "bat and?" or "ball and?". There is a definitive way". No, sorry pal, but there just isn't.
Yes, I think you are right and that is where I am getting confused, especially where it is a number that is more than one and less than another - in other words, as you have stated, it depends on what context it is in, and that's where it gets confusing. So my maths teacher friend was right in saying it is 6<x<8 for a number that is in between 6 and 8, or if say it was one of any number between say 3 and 9 it would be written as 3<x<9 - please say that that is correct or I will have to shoot myself as suggested by GB. 
(now where's that OC template)
Here's an easier one, I have to build a new house to fill a 10m2 plot but the client doesn't like squares and it has to be as big inside as possible. What shape do I have to make it to satisfy that criteria?
