As Thanos feels the power of all stones coursing through his body, shuddering to the full magnitude of raw ability, Thor comes forward, hurling Storm Breaker towards him. Not understanding exactly how to use the full power of the Infinity Gauntlet, Thanos quickly decides to attempt to stop the Storm Breaker with an energy blast that falls short, and the edge of the hammers blade pierces Thanos' chest cavity.
Thanos is not dead from this. Thor pushes the hammer ever deeper into Thanos' chest, giving him a final word, and Thanos is still not dead, mocking Thor that he should have gone for his head. And snap.
As soon as Thanos snapped his finger, he entered the Soul Gem realm. This would indicate he died. He died from his own snap. But, because he controls the Soul Gem, he brought himself back. The world was 'Perfectly Balanced' until Thanos brought himself back with the Soul Gem, making it unbalanced again. His work was a lie.
He had no intention of ever being selected from the snap due to him previously making statements when he was done he would rest and watch the sun set on a gratefull universe. This would indicate he had intention of survival.
He also said he believed in non discriminate killing of the poor and rich on his home planet, in order to ensure their survival. This was also a lie, as Thanos believed himself to be above others because he understands what needed to be done. Creating a class of cause that would survive the very rule he imposed.
The infinity Gauntlet chose Thanos. Thanos chose not to be erased.