You are right, your friend is wrong. There is a limited number of known stable elements, any periodic table contains them all.
As I know such discussions you need some kind of proof :wink:
Atoms of any element when heated emit light of known wavelengths. Thus we can compare elements present on Earth with those present on Sun and on any other star, no matter how far it is. All spectral data known can be interpreted in terms of known elements - that confirms our knowledge is complete and there are no other elements in known observable universe.
Best,
Borek
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