Saiyans! The Illogicy!

Does anyone else here find it hard to believe that only these Saiyans survived:

1. Goku (Kakarot)
   
2. Vegeta
   
3. Nappa
   
4. Raditz
   
5. Tarble (Vegeta's Brother)
   Possibly including:
   
6. Broly
   
7. Turles

(Did I miss any?)

Now, it's been said a lot of times that every Saiyan died in the explosion except for those few and HA! I've found it: The Saiyans that died in the explosion were the ones on planet Vegeta, not, I don't believe that what Vegeta says about all his race being gone is entirely accurate, Frieza told him that a Asteroid destroyed the planet (and it was Frieza) it's no surprise Vegeta would assume that his whole race died.

BUT! It still makes no sense, theoretically there would be very few Saiyans on the Planet as they are always away doing Frieza's bidding or are sent to weaker planets as babies (Like Kakarot) and this means that not every Saiyan died and there are possibly more out there in the Universe like Broly, Turles and Tarble.

What do you think?
Are they the only surviving Saiayns or does it make sense that there are more out there?

You forgot one that didn't died by the hands of freeza and that is broly's fathar paragus or something...

And i think you are right:)

Yea it's bull that they only "survived".
I am sure there are a lot more.
Goku's not the only Saiyan baby that was send to a planet and other Saiyans were fighting on other planets aswell.

Yeah, I would wonder though, if these Saiyans even knew they were Saiyans and none of them are strong like the Earth Saiyans or they'd be able to feel the presence of these people.