Question

∀a∃x, x=a^2

I think this is true right?

Answer 1

correct

Answer 2

you give me any a
and ill find a x such that x = a^2

Answer 3

so that means there is a specific x for the a^2?

Answer 4

yes namely a^2
another way of asking this is
"for any number is the square of that number a number?"

Answer 5

Which basically means that yes, there is always a number

Answer 6

of course

Answer 7

Alright, thanks :D

Answer 8

unless we are told something like this
\[a\in\{1,2,3\},x\in\{1,2,3\}\]

Answer 9

what does the E mean?

Answer 10

there exists
the sentence in english is
for any a given there is an x such that x = a^2

Answer 11

for any a given there exists a x such that x = a^2

same thing...

Answer 12

\[\forall a\exists x,|x|=a\]
is this true?

Answer 13

I think so...

Answer 14

actually, no. i don't think it is since the x can be negative, meaning that you are changing it form negative to positive

Answer 15

correct

Answer 16

so a=-3 would be such an a that would be a counterexample to that statement

Answer 17

Making the -3 a +3 which would change the value of the X

Answer 18

i see now, thanks

Answer 19

well its more that there is no x that makes this true
|x|=-3
because |x|>=0 always

Answer 20

Yup, i think i understand, luckily this won't be on my test