While
友達と会っていく
Means something like: Will meet friend some time (intention.)
Although, I think it'd be better to say:
もっと友達と会っていく
Which means something along the lines of:
Will meet with friend more (with aspect to the future.)
The 「ていく」 grammar is used as "will" or "shall" of some sort, but with future in mind.
"I will eat breakfast" should be translated as 「朝ご飯は食べる」 (asagohan wa taberu), not as 「朝ご飯は食べていく」 (asagohan wa tabete-iku).
This hard to understand because of the few number of examples, but if you look at the examples closely, the given examples actually make sense.
（１） 冬に入って、コートを着ている人が増えていきます。
- Entering winter, people wearing coat will increase (toward the future).
（２） 一生懸命、頑張っていく！
- Will try my hardest (toward the future) with all my might!
"To increase" and "to do your best" are a verb and an expression that pay special attention to the future,
however this may be case, it is still possible to say 増える (fueru) and 頑張る (ganbaru).
These are solely my thoughts, so don't take them too seriously. It would be very much appreciated if somebody could correct me if I'm wrong, or give their own thoughts on the matter.
友達と会いに行く Literally means: Go
友達と会いに行く
Literally means: Go to meet friend.
While
友達と会っていく
Means something like: Will meet friend some time (intention.)
Although, I think it'd be better to say:
もっと友達と会っていく
Which means something along the lines of:
Will meet with friend more (with aspect to the future.)
The 「ていく」 grammar is used as "will" or "shall" of some sort, but with future in mind.
"I will eat breakfast" should be translated as 「朝ご飯は食べる」 (asagohan wa taberu), not as 「朝ご飯は食べていく」 (asagohan wa tabete-iku).
This hard to understand because of the few number of examples, but if you look at the examples closely, the given examples actually make sense.
（１） 冬に入って、コートを着ている人が増えていきます。
- Entering winter, people wearing coat will increase (toward the future).
（２） 一生懸命、頑張っていく！
- Will try my hardest (toward the future) with all my might!
"To increase" and "to do your best" are a verb and an expression that pay special attention to the future,
however this may be case, it is still possible to say 増える (fueru) and 頑張る (ganbaru).
These are solely my thoughts, so don't take them too seriously. It would be very much appreciated if somebody could correct me if I'm wrong, or give their own thoughts on the matter.