/sci/ - Science & Math

>>15551117
ty anon. how can i show [math]5^{n+1} \geq 2^{n+1} + 3^{n+1} [/math] if i know [math] 5^n \geq 2^n + 3^n [/math] ?

i was trying [math]5(5^n) \geq 5(2^n + 3^n) [/math] but i cant manage to get the RHS to match

>>15480623
i feel the same, it says for all x. maybe it is being tricky where the antecedent is false for all x except 0, making the implication true?

the contrapositive makes a lot more sense to me: for all x, if x != 0 then there exists a y such that xy != x.

in this way i understand finding a single value of y, eg any value other than 1.

but in the form i gave, it is confusing.

for all x, if for all y, xy=x, then x = 0.
i guess in this case it still works because for any value of x other than x = 0, the antecedent is false, so the implication is automatically true?