The number line for the notation in example 6 would show an open dot on –2 on the left and a solid dot on 4 at the right, with a line going between them. x ≥ –17 is written as [–17, ∞), The answer is:  [5, 10] You may make other uses of the content only with the written permission of the author on payment of a fee.
Similarly, for inequalities with one value and with the "less than" symbol (such as x < 10), there are a finite amount of positive values but an infinite amount of negative values that are less than 10. that ad with the guy in the suit sitting with the kids, takes an order of fish by trying not to count them, Alasdair Williams spells this out brilliantly, check out this explanation of "Planck Time. He then poses a question: can the numbers of any one set be rearranged in such a way that they create an entirely new set not contained within the original infinite set? In other words, it shows: –3 < x ≤ 5. The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. As an actuarial friend of mine put it to me last night, "Between any two finite points, there is an infinite and uncountable set of numbers between those two endpoints.". Conclusion: It's impossible to create a one-to-one correspondence between counting numbers and every possible real number. 10 is greater than the long length, the long length is greater than the short length, the short length is greater than 0. So, the lowest value for the inequality is placed on the left side in each set of parentheses or brackets. You have already completed the quiz before. I'd also recommend "The Hilbert Hotel" by Steve Strogatz, which outlines the work of mathematician Georg Cantor in a way much more eloquent than anything I would dare summarize. So far, all of the sets we've dealt with have been "countable," which means that all the terms can be associated with a natural number {0, 1, 2, 3, 4, 5, etc ...} To get to a bigger infinity, we need to come up with something that is uncountably infinite (i.e. You may also want to see our posts on graphing and quadratics. Place the insertion pointer at where you want to insert the symbol. the sides to a circle). Correspondence is a concept in set theory that works by relating each individual item in one set to an individual item in another set. You will notice that the numbers and symbols in interval notation are written in the same order as a number line. This is called "cardinality" and it leads to the smallest type of infinity, which we like to call ... Before we go on, I have to stop for a second and say this post is heavily indebted to Alasdair Wilkins' outstanding essay, "A Brief Introduction to Infinity. The answer's not infinity plus one. Why Infinity Plus One Isn't Bigger Than Infinity. is less than > > is greater than ≮ \nless: is not less than ≯ \ngtr: is not greater than ≤ \leq: is less than or equal to ≥ \geq: is greater than or equal to ⩽ \leqslant: is less than or equal to ⩾ If your megger is reading "OL" (over load) or "I" (infinity), these are commonly used readings on megohmmeters, when the measurement exceeds the maximum indicated value of the tester. You may  want to see our posts on number lines and inequalities. We use the following symbols for interval notation: We use the symbols (  ) and  [   ] in interval notation.