Density and Limits
What is the density property?
You can always find a number in between any two numbers in the set.
1/2 + 1/2
1
write 2^3 in expanded form and solve
2x2x2=8
What sets of number have the density property and which don't?
Do: Rational, Real
Don't: Natural, Whole, Integers, Irrational
I have hands but no arms, a face but no head, and I tell you what to do without saying a word.
What am I?
A clock
What is the limit of {0,1,2,3,...}
Infinity
3/4 + 2/3
4/3
Write as a simplified exponent (2)^3 x (2)^4
Write the set of numbers that has a limit of negative infinity
varies
The more you take from me, the bigger I get.
What am I?
A hole
Do the integers have the density property?
No!
3/4 x 5/8
15/32
Write as a simplified exponent (3)^5 divided by (3)^2
(3)^3
Are the answers to both questions the same
1. (-2)^2
2. -2^2
No!
I can be cracked, made, told, and played.
What am I?
A joke
What is the limit of {1/2, 1/3, 1/4, ...}
0
1/2 divided by 3/4
2/3
Write as a simplified exponent (5^4)^2
5^8
12k^2m^8 divided by 4km^5
3km^3
I speak without a mouth, hear without ears, and repeat whatever you say.
What am I?
An echo
What is the limit of {2.1, 2.01, 2.001, 2.0001, ...}
2
1/2 + 3/4 - 2/3 - 4/3
-3/4
x^2y^3 x x^4y^1
x^6y^4
4d^4w^3 x 6dw^4
24d^5w^7
I can only be given,
never taken.
Once I’m broken,
I’m almost impossible to fix.
What am I?
Trust